graphical representation of educational data

A Review on Visualization of Educational Data in Online Learning

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• M. Ali Akber Dewan 17 ,
• Walter Moreno Pachon 17 &
• Fuhua Lin 17  

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Higher educational institutions capture huge amounts of educational data, especially in online learning. Data mining techniques have shown promises to interpret these data using different patterns . However, understanding the mining patterns and extracting meaningful information from the data require reasonable skills and knowledge for the users. Information visualization, due to its potential to display large amount of data, may fill this gap. In this paper, we present a short review of such visualization systems that focus on extracting meaningful information from the educational data. Visualizations have been used in different applications dealing with educational data, especially for monitoring student performance, understanding learning style, analyzing course and program status, and dropout prediction. In this paper, we reviewed the existing visualization systems, their design considerations, and their strengths and weaknesses to analyze educational data in the context of online learning. Research findings indicate that although some progress has been achieved in educational data mining and visualizations, designing and developing effective and easy to understand visualizations and having the functionalities of interactivity and time-series analysis are still challenging. This review provides insight into how to build a learner and instructor focused effective visualization system for an online learning environment.

• Information visualization
• Educational data mining
• Pattern recognition
• Learning management system
• Visual analytics

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This research was supported by NSERC Discovery Grant, and Academic and Professional Development Grant, Athabasca University, Canada.

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Dewan, M.A.A., Pachon, W.M., Lin, F. (2021). A Review on Visualization of Educational Data in Online Learning. In: Pang, C., et al. Learning Technologies and Systems. SETE ICWL 2020 2020. Lecture Notes in Computer Science(), vol 12511. Springer, Cham. https://doi.org/10.1007/978-3-030-66906-5_2

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Graphical representations: Helping students interpret data

The process of statistical investigation may be conceptualized as having four components: Posing the question, collecting the data, analyzing the data, and interpreting the data. Graphical representations of data are a critical part of the analysis phase, since the use of different representations communicates information in different ways. This chapter discusses instructional strategies for moving between three different pairs of representations: bar graphs showing ungrouped data and standard bar graphs, line plots and bar graphs, and stem-and-leaf plots and histograms. These strategies are designed to optimize the accuracy of interpretations and avoid common pitfalls in making sense of the data; the strategies focus on reading rather than on making the representations themselves. Students' attempts to make the translations between representations are discussed within the framework of the instructional suggestions.

The CAUSE Research Group is supported in part by a member initiative grant from the American Statistical Association’s Section on Statistics and Data Science Education

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An Analysis of Graphical Representation of Data in Elementary School Mathematics Textbooks

The paper aims to present the research on the frequency and prevalence of graphical representations of data in Czech elementary education mathematic textbooks. Textbooks were selected based on the presence of a note of approval granted by The Ministry of Education, Youth and Sports of the Czech Republic. Eighty-four textbooks (and workbooks where available) were analysed, with 2760 graphical representations of data identified. These representations were coded into seven types and 14 subtypes with a combination of apriori and emergent coding. Graphical representations of data are affluent in local mathematics textbooks. They follow logical routes of introduction, with pictorial unit graphics common in the early grades, taking the form of proto-graphs later. Bar graphs and pie graphs are the most common types of fully developed graphs identified in the source materials. The outputs will serve as a base for further study in the area, as the ways of building data visualisation literacy are not yet sufficiently explored and described in the local context of elementary education.

Keywords: Primary education , mathematics , data visualisation literacy , graphs , Czech Republic

Introduction

Visual representations of data play a crucial role in our civic lives. Recent global covid-19 pandemics went hand-in-hand with a flood of visualised data, as the emergency asked for fast and reliable ways to report and communicate up-to-date numbers. The recent geopolitical situation in Europe is also unravelling during the times when the topic of disinformation gains its spotlight – and data visualisation can be misused to fuel disinformation and manipulate its readers ( McNutt et al., 2021 ) while exploiting our inbuilt trust in data. In light of these events, we stress the need for data visualisation literacy (DVL). DVL is defined as "" ( Lee et al., 2017, p. 552 ; for more definitions, see Börner, 2019 ) and can be seen as a part of broader data literacy and an extension of more established visual literacy.

The need to develop the ability to interpret and generalise from data graphics has already been discussed for decades ( see Curcio, 1987 ), and visual data comprehension is a long-standing topic in the education area ( already discussed in Strickland, 1938 ). Still, a high portion of the population performs low on critical aspects of data visualisation literacy and has difficulties interpreting graphical representations of data in media or textbooks ( Börner et al., 2016 ).

Problem Statement

While some attention already has been paid to the research and development of instructions for strengthening visualisation literacy among the adult public, the topic has not yet been addressed much in primary education. DVL in the context of primary education receives meagre attention and is currently dealt with by only a handful of researchers ( e.g., Alper et al., 2017 ; Chevalier et al., 2018 ; Shreiner, 2020 ). Visual literacy shows no better treatment ( as noted by Guo et al., 2018 ). Primary education is where the fundamentals of our data visualisation skills should be built. By the fourth grade, children should have all the knowledge and skills necessary for reading graphs ( Curcio, 1987 ). However, we are not even sure how and in what forms data visualisations are present in our educational materials. Graphics are ubiquitous in textbooks ( Fingeret, 2012 ; Roberts et al., 2013 ) and "" ( Fingeret, 2012, p. 2 ) and this also applies to graphical representations of quantitative data.

Although some content analysis studies already focus on graphical data representations in elementary education textbooks ( e.g., Alper et al., 2017 ; Fingeret, 2012 ; Shreiner, 2017 ), there are no studies conducted in the local context of Czech educational materials. Data visualisation literacy is not even a topic yet in Czechia, even though broader data literacy is currently a prominent theme amid recent curricular developments in the country. Currently, state standards in the Czech Republic mention data visualisation and the ability to interpret and create data graphics as an essential skill that should be developed ( MŠMT, 2022 ), but they do not provide any guidance ( same as reported for US standards by Shreiner, 2020 ).

The research presented here will constitute a first step in understanding the current state of primary-level DVL development in the local context of the Czech formal education system. It will serve as a base for further inquiry into the area. Our primary research questions for this analysis are as follows: what types of graphical representations of data are present in Czech elementary mathematics textbooks? How common are they? In what chronology do they familiarise students with visual representations of data? Furthermore, what terminology is used for data visualisation objects in these textbooks?

Research Methods

To answer these questions, we conducted a content analysis of primary education mathematics textbooks. The method was selected as a first step in deepening our understanding in this area because, as Coleman ( 2016 ) reported, teachers' most frequently used instructional practices while working with graphical representations (including data visualisations) were to point to or refer to graphical representations in textbooks. Textbooks are also regarded as materials with the highest influence on what happens in classrooms ( Son & Diletti, 2017 ). This chapter will present the stages of our research in detail.

Selecting textbooks for analysis

We decided to analyse mathematics textbooks because "certain aspects of visualisation literacy are taught as early as at elementary school, where children learn to read basic charts and graphs in mathematics and science classes" ( Alper et al., 2017, p. 5485 ). Furthermore, based on local state standards for elementary education and relevant curricular documents, mathematics is the area that should lead children to educational outcomes in data visualisation skills. Our focus was on the most neglected grades in terms of data visualisation research: grades 1 to 5 of elementary school.

We chose complete series of textbooks, together with workbooks where available. Only materials validated by (editions with a valid note of approval granted by the ministry at the time of the analysis) were selected and analysed. Five complete textbook series from four different publishers were also chosen based on our consultation with professional subject librarians, physical availability and local usage. Eighty-four textbooks and workbooks were analysed, with 5528 pages total (see Table 1).

Defining graphical representations of data

Not all visuals used in textbooks are graphical representations of data. For our research, graphical representations of data are visual displays of quantitative information, e.g., any graphic that shows quantitive data and its visual variables are influenced by numerical inputs. These graphics could also be called, as used by Chevalier et al. ( 2018 ). Visual variables influenced by input data are a crucial part of the definition because data visualisation terminology is famously inconsistent. Different sources use the terms,, or quite freely, and the situation is the same in the Czech language: '' and '' can be used interchangeably. Furthermore, ' (in Czech ') is a term from graph theory, making the terminological landscape even foggier. For different approaches to defining charts, graphs and data visualisations, see Friel et al. ( 2001 ).

This variety can be counterproductive when creating a classification of graphical data representations for the sake of content analysis: for example, Fingeret ( 2012 ) developed a class named, which contains pie, bar and line together with a "" (p. 29), which is traditionally used as a visual metaphor of a hierarchy and its visual variables are usually not directly influenced by quantitative data. On the other hand, a pyramid (sometimes referred to as a sorted two-way histogram) is a type where individual steps of the pyramid change their height or weight based on input data ( see Harris, 1999 ). Discerning between those terms is often complicated and can lead to many confusions. This fact also led us to one of our research questions: while analysing the frequency and prevalence of different types of graphical representations of data, we also wanted to look into what terms are used to describe them.

During the analysis, we marked some graphics as ' – meaning they work as graphical devices as defined by Roberts et al. ( 2013 ): "" (p. 17), i.e., they are fully developed statistical graphics with all the components that usually constitute it. This notation enables us to further differentiate between more advanced graphical representations of data and simpler data-driven graphics that may utilise the same visual variables while serving as proto-graphs.

Classification and rules for coding

First, a small and various exploratory sample of textbooks from selected series and grades was chosen, pre-analysed and validated with a fellow reviewer to clarify ambiguous items. Based on this pre-sample, the priori classification of visual data representations was created while being informed by existing classifications used in analysis up-to-now ( esp. Alper et al., 2017 ; Burrows & Cooper, 1987 ; Shreiner, 2017 ) and while consulting the leading reference guides from the domain ( mainly Harris, 1999 ). This classification created a base for our analysis with definitions and examples for each data graphic type. When a new type of graphical representation emerged later during the data collection, the classification was updated to encompass the complex reality of graphics used in Czech elementary mathematics textbooks and workbooks. Graphical representations of data were coded into seven main types, including a total of 14 specific subtypes (for a complete list of types and subtypes, see).

The rules were developed for coding. For every object, we noted its type, page, terminology, level of visual abstraction, and role. As noted in Burrows and Cooper ( 1987 ), both interpretation and construction of graphs are essential, and the necessity to focus on both is stressed. That is why we also decided to code the role of graphical data representations in textbooks. We noted where textbooks asked children to complete a graphic, such as drawing in a series of symbols to represent data or filling a part of an empty pie graph with colour. These visuals were listed as. In cases where data graphics were used solely to present data for an exercise and were intended to be read rather than visually altered or completed, we labelled them. They were labelled as when used in explanation sections (presenting the subject matter, not part of an exercise). The level of visual abstraction was adopted from Alper et al. ( 2017 ) and Burrows & Cooper ( 1987 ) and also noted during coding as well, i.e., whether the graphical object used pictures of real-life entities, illustrations or abstract shapes to represent numerical data.

Results and analysis

In total, 2760 graphical representations of data were logged during our analysis, together with their observed properties. Frequencies were calculated for all the types. Frequencies were then split by grades to analyse the prevalence of different types in different levels of primary education ().

Pictorial units

Pictorial units present data with pictographs, which can be unstructured (free-form pictographs, 18.73 % of all graphical representations of data), or they can be organised non-randomly (structured pictographs, 27 % of all graphical representations). There were 517 free-form pictographs (FP) in the sample, peaking in presence in G1 (64.02 % of all FP) and then gradually leaving the textbooks as grade progressed, with 23.60 % of all FP present in G2 and <2% in G5. In G1, free-form pictographs are the most salient type, with 41.48% of all the data graphics used in G1 textbooks and workbooks. Structured pictographs are common even in higher grades, peaking also in G1 (38.10 % of all representations in G1), but only slowly declining in presence till G4 (21.72 % of all G4 graphics). In Czech mathematics textbooks, we identified a particular type of illustrated structured pictograph that we traced separately: abacus, primarily used to visually represent place values when working with bigger numbers (thus peaking in presence in grade 3 (5.43 % of all G3 graphics).

Numbered lines

Numbered lines are a common simple way of visualising data, being steadily present through all five grades while being the most salient visual representation in G4 (40.29 % of all G4 representations). Most of the numbered lines are used in a constructional way (44.08 % of all numbered lines), followed by interpretative usage (32.10 %) – see. In our classification, we defined a specific subtype,, that is, in fact, an illustrated numbered line; This visual metaphor was present as a small number of cases (0.36 % of all graphics).

Part-whole graphics

There were 526 part-whole (PW) graphics in our sample. PW graphics can often be seen as a preparatory stage to understand more abstract and developed part-whole data visualisations (such as treemaps), with pie graphs being the most interesting sub-type here. Regular PW graphics (mostly rectangular data graphics; namely fraction diagrams and other part-whole items, such as area models and decimal area models) were the most common subtypes (). Separately, we noted a specific type of PW graphic that was in the end quite rarely used in Czech textbooks: bar models (only 1.34 % of all graphics, peaking in G3 with 3.76 % of all graphics used in this grade).

There were 166 pie graphs in total, mainly used when presenting and practising fractions. First pie graphs are presented as early as G2, peaking in G4 (19.03 % of all data graphics in G4). Out of all pies, there were only 12.05 % of pie graphs; 45 % of those were used interpretatively and 40 % in exercises (where n pie = 20). In analysed textbooks, pie graphs were addressed as or ( or, but never as,).

There were 134 bar graphs in our sample, including four histograms (i.e., particular type of joined column graph), classified as a subtype here with regard to Harris ( 1999 ). As the Czech language does not differentiate betweengraphs and graphs, we were tracking them under the joined type of. Bar graphs are the second most prevalent subtype in G5 (with 15.73 % of all G5 data graphics scoring second after numbered lines in this grade). Out of 130 regular bar graphs, there were 125 ones, of which 50.40 % were used constructionally. Even here, the words and are used freely, with the attribute 'sloupcový' or 'sloupkový' (Czech variants of). Interesting was the use of level of abstraction: pictorial proportional bar graphs (e.g., using differently sized trees in place of bars) were present in five cases. In three cases, these illustrated graphs were called (). Two out of four recorded histogram cases were also calledin textbooks.

Line graphs

Line graphs are gradually introduced into the textbooks: we traced first line graphs as early as G2, but they are most prevalent in G5 (making 9.39 % of all G5 data graphics). All identified line graphs were ones. 40.82 % of line graphs were used interpretatively, 53.06 % were used constructionally, and 6.12 % were used as part of explanation sections of textbooks. Same as with other types, words and are used indiscriminately here, with attribution used where specified (translated freely as with join line between two points). In two cases, the term was used as the graphical representation dealt with timetable data.

Point graphs

Point graphs are a specific type of data visualisation that utilises points (or dots) to visualise data. In this category, we classified dot plots (functionally similar to bar graphs, with the difference being the visual variable of position used instead of length) and scatterplots. Scatterplots are marginally present in our sample since G3, peaking in G5 (5.40 % of all G5 representations), where they are utilised to work with coordinates. They were never called or in our sample, same as dot plots – those were addressed solely asor.

Our analysis showed that various graphical representations of data are affluently present in Czech elementary mathematics textbooks and workbooks. Children in G5 can be already familiar with pie graphs, line graphs, bar graphs, point graphs, and in some cases, even specific subtypes such as histograms. As Coleman ( 2016 ) discovered, " [and frequently]" (p. 209). She was analysing teachers' reported overall use of graphical representations, and bar graphs were approached solely as fully-developed graphs, but we can agree that situation in our sample is similar: out of 228 fully-developed graphs of various types, there were 129 bar graphs (56.58 %).

The introduction of different types of graphical representations follows the recommendation by Burrows and Cooper ( 1987 ). They state that representations should be established in logical sequence from simple to more complex, e.g., starting with simple pictorial units, then using structured pictographs and later moving to bar graphs and more developed graphs. Indeed, graphical representations follow a logical path in our sample, starting with free-form pictographs in early grades, then becoming more structured and fully developed later on. This logical sequence can be illustrated with bar graphs, where children are gradually prepared to understand them by structured pictographs, which are also common in Czech mathematics textbooks during early grades (as reported in). Terms used for fully-developed graphs are varied, as it reflects the messy reality of the field. There is no clear distinction between and in the analysed textbooks, and we believe this lack of distinction is constrictive. However, that is not the fault of textbooks, as it is a known issue in our domain.

Further inquiry

The sole presence of a graph is essential in familiarising the children with such a visual form but building a robust DVL is a much more varied task. The critical part is the context and the process: we argue that data visualisation skills are useless without grasping the data literacy preceding it. Even from the point of view of a reader: when I do not understand the fabric of data behind the visuals and when I am not familiar with data collection and transformation processes and their limitations, I cannot ever fully assess and critically evaluate the graph I am looking at. This is even more apparent from the point of view of a creator.

The first step is to develop DVL in a real context – Shah and Hoeffner ( 2002 ) included in their implications for teaching graphical literacy skills the goal to teach them, as teaching them abstractly may not make students able to apply them later in the real context of science (or any other context). In our sample, we found several cases where instructions utilised abstract data in graphs without any context (e.g., readfrom a graph, draw in into a graph), but the situation will have to be further analysed. In future studies, it will be beneficial to focus more closely on fully-developed graphs and their functions in textbook exercises, together with what type of data they are utilising and in what ways.

Curricular developments in the Czech republic's education system are an opportunity for interconnecting classes and fields, which means more opportunities for graphical representations of data in other fields than mathematics. In further studies, it will also be beneficial to broaden the analysis to textbooks in other elementary subjects, i.e., widen the scope into science and social studies textbooks, and compare the findings between disciplines.

Another step will be to analyse data-driven graphics as a part of a broader data literacy teaching process. There are examples in our sample that could be marked as interesting in terms of introducing children to data processes. One notable example is a pie graph used for a complex process of data collection, abstraction and data transformation. The task begins with making a timetable of a regular day in terms of picking the most salient regular activity for every hour. These activities are assigned colours and then filled into a stripe of paper divided into 24 squares (data can be grouped by activity), forming a stacked bar graph. The stripe is then glued into a paper loop, and a circle is drawn with the same diameter as the paper one. Marks on the circle are drawn based on the data on the paper loop. This way, the base for a pie chart is created, and a fully-developed graph can now be constructed by connecting marks on the circle with its centre point. The presented process includes data collection, transformation, and choosing a relevant visual metaphor to present the data. Further deeper qualitative content analysis of fully-developed graphs in textbooks would contribute to understanding how data literacy and connected DVL are developed in primary education. As Brugar and Roberts ( 2017 ) implies, the final goal is to find fruitful ways to guide teachers in cultivating visual literacy and data visualisation literacy in children effectively.

Acknowledgments

The presented results are a part of a specific project called Content analysis of textbooks for the first level of elementary school with a focus on the development of skills in visualisation literacy with financial support from the University of Hradec Králové.

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Son, J.-W., & Diletti, J. (2017). What Can We Learn from Textbook Analysis? In J. -W. Son, T. Watanabe, & J. -J. Lo (Eds.), What Matters? Research Trends in International Comparative Studies in Mathematics Education (pp. 3-32). Springer International Publishing.

Strickland, R. G. (1938). A study of the possibilities of graphs as a means of instruction in the first four grades of the elementary school. Teachers College Press.

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Education, educational psychology, pedagogy, positive pedagogy, special education, second language teaching

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Marek, T., & Maněnová, M. (2022). An Analysis of Graphical Representation of Data in Elementary School Mathematics Textbooks. In A. Güneyli, & F. Silman (Eds.), ICEEPSY 2022: Education and Educational Psychology, vol 3. European Proceedings of International Conference on Education and Educational Psychology (pp. 174-183). European Publisher. https://doi.org/10.15405/epiceepsy.22123.15

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2: Graphical Representations of Data

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In this chapter, you will study numerical and graphical ways to describe and display your data. This area of statistics is called "Descriptive Statistics." You will learn how to calculate, and even more importantly, how to interpret these measurements and graphs.

• 2.1: Introduction In this chapter, you will study numerical and graphical ways to describe and display your data. This area of statistics is called "Descriptive Statistics." You will learn how to calculate, and even more importantly, how to interpret these measurements and graphs. In this chapter, we will briefly look at stem-and-leaf plots, line graphs, and bar graphs, as well as frequency polygons, and time series graphs. Our emphasis will be on histograms and box plots.
• 2.2: Stem-and-Leaf Graphs (Stemplots), Line Graphs, and Bar Graphs A stem-and-leaf plot is a way to plot data and look at the distribution, where all data values within a class are visible. The advantage in a stem-and-leaf plot is that all values are listed, unlike a histogram, which gives classes of data values. A line graph is often used to represent a set of data values in which a quantity varies with time. These graphs are useful for finding trends.  A bar graph is a chart that uses either horizontal or vertical bars to show comparisons among categories.
• 2.3: Histograms, Frequency Polygons, and Time Series Graphs A histogram is a graphic version of a frequency distribution. The graph consists of bars of equal width drawn adjacent to each other. The horizontal scale represents classes of quantitative data values and the vertical scale represents frequencies. The heights of the bars correspond to frequency values. Histograms are typically used for large, continuous, quantitative data sets. A frequency polygon can also be used when graphing large data sets with data points that repeat.
• 2.4: Using Excel to Create Graphs Using technology to create graphs will make the graphs faster to create, more precise, and give the ability to use larger amounts of data. This section focuses on using Excel to create graphs.
• 2.5: Graphs that Deceive It's common to see graphs displayed in a misleading manner in social media and other instances. This could be done purposefully to make a point, or it could be accidental. Either way, it's important to recognize these instances to ensure you are not misled.
• 2.E: Graphical Representations of Data (Exercises) These are homework exercises to accompany the Textmap created for "Introductory Statistics" by OpenStax.

Contributors and Attributions

Barbara Illowsky and Susan Dean (De Anza College) with many other contributing authors. Content produced by OpenStax College is licensed under a Creative Commons Attribution License 4.0 license. Download for free at http://cnx.org/contents/[email protected] .

Guide On Graphical Representation of Data – Types, Importance, Rules, Principles And Advantages

What are Graphs and Graphical Representation?

Graphs, in the context of data visualization, are visual representations of data using various graphical elements such as charts, graphs, and diagrams. Graphical representation of data , often referred to as graphical presentation or simply graphs which plays a crucial role in conveying information effectively.

Principles of Graphical Representation

Effective graphical representation follows certain fundamental principles that ensure clarity, accuracy, and usability:Clarity : The primary goal of any graph is to convey information clearly and concisely. Graphs should be designed in a way that allows the audience to quickly grasp the key points without confusion.

• Simplicity: Simplicity is key to effective data visualization. Extraneous details and unnecessary complexity should be avoided to prevent confusion and distraction.
• Relevance: Include only relevant information that contributes to the understanding of the data. Irrelevant or redundant elements can clutter the graph.
• Visualization: Select a graph type that is appropriate for the supplied data. Different graph formats, like bar charts, line graphs, and scatter plots, are appropriate for various sorts of data and relationships.

Rules for Graphical Representation of Data

Creating effective graphical representations of data requires adherence to certain rules:

• Select the Right Graph: Choosing the appropriate type of graph is essential. For example, bar charts are suitable for comparing categories, while line charts are better for showing trends over time.
• Label Axes Clearly: Axis labels should be descriptive and include units of measurement where applicable. Clear labeling ensures the audience understands the data’s context.
• Use Appropriate Colors: Colors can enhance understanding but should be used judiciously. Avoid overly complex color schemes and ensure that color choices are accessible to all viewers.
• Avoid Misleading Scaling: Scale axes appropriately to prevent exaggeration or distortion of data. Misleading scaling can lead to incorrect interpretations.
• Include Data Sources: Always provide the source of your data. This enhances transparency and credibility.

Importance of Graphical Representation of Data

Graphical representation of data in statistics is of paramount importance for several reasons:

• Enhances Understanding: Graphs simplify complex data, making it more accessible and understandable to a broad audience, regardless of their statistical expertise.
• Helps Decision-Making: Visual representations of data enable informed decision-making. Decision-makers can easily grasp trends and insights, leading to better choices.
• Engages the Audience: Graphs capture the audience’s attention more effectively than raw data. This engagement is particularly valuable when presenting findings or reports.
• Universal Language: Graphs serve as a universal language that transcends linguistic barriers. They can convey information to a global audience without the need for translation.

Advantages of Graphical Representation

The advantages of graphical representation of data extend to various aspects of communication and analysis:

• Clarity: Data is presented visually, improving clarity and reducing the likelihood of misinterpretation.
• Efficiency: Graphs enable the quick absorption of information. Key insights can be found in seconds, saving time and effort.
• Memorability: Visuals are more memorable than raw data. Audiences are more likely to retain information presented graphically.
• Problem-Solving: Graphs help in identifying and solving problems by revealing trends, correlations, and outliers that may require further investigation.

Use of Graphical Representations

Graphical representations find applications in a multitude of fields:

• Business: In the business world, graphs are used to illustrate financial data, track performance metrics, and present market trends. They are invaluable tools for strategic decision-making.
• Science: Scientists employ graphs to visualize experimental results, depict scientific phenomena, and communicate research findings to both colleagues and the general public.
• Education: Educators utilize graphs to teach students about data analysis, statistics, and scientific concepts. Graphs make learning more engaging and memorable.
• Journalism: Journalists rely on graphs to support their stories with data-driven evidence. Graphs make news articles more informative and impactful.

Types of Graphical Representation

There exists a diverse array of graphical representations, each suited to different data types and purposes. Common types include:

1.Bar Charts:

Used to compare categories or discrete data points, often side by side.

2. Line Charts:

Ideal for showing trends and changes over time, such as stock market performance or temperature fluctuations.

3. Pie Charts:

Display parts of a whole, useful for illustrating proportions or percentages.

4. Scatter Plots:

Reveal relationships between two variables and help identify correlations.

5. Histograms:

Depict the distribution of data, especially in the context of continuous variables.

In conclusion, the graphical representation of data is an indispensable tool for simplifying complex information, aiding in decision-making, and enhancing communication across diverse fields. By following the principles and rules of effective data visualization, individuals and organizations can harness the power of graphs to convey their messages, support their arguments, and drive informed actions.

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FAQs on Graphical Representation of Data

What is the purpose of graphical representation.

Graphical representation serves the purpose of simplifying complex data, making it more accessible and understandable through visual means.

Why are graphs and diagrams important?

Graphs and diagrams are crucial because they provide visual clarity, aiding in the comprehension and retention of information.

How do graphs help learning?

Graphs engage learners by presenting information visually, which enhances understanding and retention, particularly in educational settings.

Who uses graphs?

Professionals in various fields, including scientists, analysts, educators, and business leaders, use graphs to convey data effectively and support decision-making.

Where are graphs used in real life?

Graphs are used in real-life scenarios such as business reports, scientific research, news articles, and educational materials to make data more accessible and meaningful.

Why are graphs important in business?

In business, graphs are vital for analyzing financial data, tracking performance metrics, and making informed decisions, contributing to success.

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9.2: Presenting Quantitative Data Graphically

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Quantitative, or numerical, data can also be summarized into frequency tables.

Example \(\PageIndex{1}\)

A teacher records scores on a 20-point quiz for the 30 students in his class. The scores are

19 20 18 18 17 18 19 17 20 18 20 16 20 15 17 12 18 19 18 19 17 20 18 16 15 18 20 5 0 0

These scores could be summarized into a frequency table by grouping like values:

Using this table, it would be possible to create a standard bar chart from this summary, like we did for categorical data:

However, since the scores are numerical values, this chart doesn’t really make sense; the first and second bars are five values apart, while the later bars are only one value apart. It would be more correct to treat the horizontal axis as a number line. This type of graph is called a histogram .

Definition: Histogram

A histogram is a graphical representation of quantitative data. The horizontal axis is a number line.

Example \(\PageIndex{2}\)

For the values above, a histogram would look like:

Unfortunately, not a lot of common software packages can correctly graph a histogram. About the best you can do in Excel or Word is a bar graph with no gap between the bars and spacing added to simulate a numerical horizontal axis.

If we have a large number of widely varying data values, creating a frequency table that lists every possible value as a category would lead to an exceptionally long frequency table, and probably would not reveal any patterns. For this reason, it is common with quantitative data to group data into class intervals .

Definition: Class Intervals

Class intervals are groupings of the data. In general, we define class intervals so that

• Each interval is equal in size. For example, if the first class contains values from 120-129, the second class should include values from 130-139.
• Each interval has a lower limit and an upper limit , e.g., for interval 120-129, 120 is the lower limit and 129 is the upper limit.
• The class width is the difference between two consecutive lower limits.
• The class width is the same for every interval in the frequency table.
• We have somewhere between 5 and 20 classes, typically, depending upon the number of data we’re working with.

Example \(\PageIndex{3}\)

Suppose that we have collected weights from 100 male subjects as part of a nutrition study. For our weight data, we have values ranging from a low of 121 pounds to a high of 263 pounds, giving a total span of \(263-121 = 142\). We could create 7 intervals with a width of around 20, 14 intervals with a width of around 10, or somewhere in between. Oftentimes, we have to experiment with a few possibilities to find something that represents the data well. Let us try using an interval width of 15. We could start at 121, or at 120 since it is a nice round number.

Notice, the class width is 15 since \(150-135 = 15\), \(165-150 = 15\), and so on.

A histogram of this data would look like:

In many software packages, you can create a graph similar to a histogram by putting the class intervals as the labels on a bar chart.

Other graph types such as pie charts are possible for quantitative data. The usefulness of different graph types will vary depending upon the number of intervals and the type of data being represented. For example, a pie chart of our weight data is difficult to read because of the quantity of intervals we used.

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The total cost of textbooks for the term was collected from 36 students. Create a histogram for this data.

$140 $160 $160 $165 $180 $220 $235 $240 $250 $260 $280 $285

$285 $285 $290 $300 $300 $305 $310 $310 $315 $315 $320 $320

$330 $340 $345 $350 $355 $360 $360 $380 $395 $420 $460 $460

When collecting data to compare two groups, it is desirable to create a graph that compares quantities.

Example \(\PageIndex{4}\)

The data below came from a task in which the goal is to move a computer mouse to a target on the screen as fast as possible. On 20 of the trials, the target was a small rectangle; on the other 20, the target was a large rectangle. Time to reach the target was recorded on each trial.

One option to represent this data would be a comparative histogram or bar chart, in which bars for the small target group and large target group are placed next to each other.

Definition: Frequency Polygon

An alternative representation is a frequency polygon. A frequency polygon starts out like a histogram, but instead of drawing a bar, a point is placed in the midpoint of each interval at height equal to the frequency. The midpoint of an interval is

\[\dfrac{\text{lower limit}_2 - \text{lower limit}_1}{2} \nonumber \]

Typically, the points are connected with straight lines to emphasize the distribution of the data.

Example \(\PageIndex{5}\)

This graph makes it easier to see that reaction times were generally shorter for the larger target, and that the reaction times for the smaller target were more spread out.

Numerical Summaries of Data

It is often desirable to use a few numbers to summarize a distribution. One important aspect of a distribution is where its center is located. Measures of central tendency are discussed first. A second aspect of a distribution is how spread out it is. In other words, how much the data in the distribution vary from one another. The second section describes measures of variability

Graphical Representation of Data

Graphical representation of data is an attractive method of showcasing numerical data that help in analyzing and representing quantitative data visually. A graph is a kind of a chart where data are plotted as variables across the coordinate. It became easy to analyze the extent of change of one variable based on the change of other variables. Graphical representation of data is done through different mediums such as lines, plots, diagrams, etc. Let us learn more about this interesting concept of graphical representation of data, the different types, and solve a few examples.

Definition of Graphical Representation of Data

A graphical representation is a visual representation of data statistics-based results using graphs, plots, and charts. This kind of representation is more effective in understanding and comparing data than seen in a tabular form. Graphical representation helps to qualify, sort, and present data in a method that is simple to understand for a larger audience. Graphs enable in studying the cause and effect relationship between two variables through both time series and frequency distribution. The data that is obtained from different surveying is infused into a graphical representation by the use of some symbols, such as lines on a line graph, bars on a bar chart, or slices of a pie chart. This visual representation helps in clarity, comparison, and understanding of numerical data.

Representation of Data

The word data is from the Latin word Datum, which means something given. The numerical figures collected through a survey are called data and can be represented in two forms - tabular form and visual form through graphs. Once the data is collected through constant observations, it is arranged, summarized, and classified to finally represented in the form of a graph. There are two kinds of data - quantitative and qualitative. Quantitative data is more structured, continuous, and discrete with statistical data whereas qualitative is unstructured where the data cannot be analyzed.

Principles of Graphical Representation of Data

The principles of graphical representation are algebraic. In a graph, there are two lines known as Axis or Coordinate axis. These are the X-axis and Y-axis. The horizontal axis is the X-axis and the vertical axis is the Y-axis. They are perpendicular to each other and intersect at O or point of Origin. On the right side of the Origin, the Xaxis has a positive value and on the left side, it has a negative value. In the same way, the upper side of the Origin Y-axis has a positive value where the down one is with a negative value. When -axis and y-axis intersect each other at the origin it divides the plane into four parts which are called Quadrant I, Quadrant II, Quadrant III, Quadrant IV. This form of representation is seen in a frequency distribution that is represented in four methods, namely Histogram, Smoothed frequency graph, Pie diagram or Pie chart, Cumulative or ogive frequency graph, and Frequency Polygon.

Advantages and Disadvantages of Graphical Representation of Data

Listed below are some advantages and disadvantages of using a graphical representation of data:

• It improves the way of analyzing and learning as the graphical representation makes the data easy to understand.
• It can be used in almost all fields from mathematics to physics to psychology and so on.
• It is easy to understand for its visual impacts.
• It shows the whole and huge data in an instance.
• It is mainly used in statistics to determine the mean, median, and mode for different data

The main disadvantage of graphical representation of data is that it takes a lot of effort as well as resources to find the most appropriate data and then represent it graphically.

Rules of Graphical Representation of Data

While presenting data graphically, there are certain rules that need to be followed. They are listed below:

• Suitable Title: The title of the graph should be appropriate that indicate the subject of the presentation.
• Measurement Unit: The measurement unit in the graph should be mentioned.
• Proper Scale: A proper scale needs to be chosen to represent the data accurately.
• Index: For better understanding, index the appropriate colors, shades, lines, designs in the graphs.
• Data Sources: Data should be included wherever it is necessary at the bottom of the graph.
• Simple: The construction of a graph should be easily understood.
• Neat: The graph should be visually neat in terms of size and font to read the data accurately.

Uses of Graphical Representation of Data

The main use of a graphical representation of data is understanding and identifying the trends and patterns of the data. It helps in analyzing large quantities, comparing two or more data, making predictions, and building a firm decision. The visual display of data also helps in avoiding confusion and overlapping of any information. Graphs like line graphs and bar graphs, display two or more data clearly for easy comparison. This is important in communicating our findings to others and our understanding and analysis of the data.

Types of Graphical Representation of Data

Data is represented in different types of graphs such as plots, pies, diagrams, etc. They are as follows,

Related Topics

Listed below are a few interesting topics that are related to the graphical representation of data, take a look.

• x and y graph
• Frequency Polygon
• Cumulative Frequency

Examples on Graphical Representation of Data

Example 1 : A pie chart is divided into 3 parts with the angles measuring as 2x, 8x, and 10x respectively. Find the value of x in degrees.

We know, the sum of all angles in a pie chart would give 360º as result. ⇒ 2x + 8x + 10x = 360º ⇒ 20 x = 360º ⇒ x = 360º/20 ⇒ x = 18º Therefore, the value of x is 18º.

Example 2: Ben is trying to read the plot given below. His teacher has given him stem and leaf plot worksheets. Can you help him answer the questions? i) What is the mode of the plot? ii) What is the mean of the plot? iii) Find the range.

Solution: i) Mode is the number that appears often in the data. Leaf 4 occurs twice on the plot against stem 5.

Hence, mode = 54

ii) The sum of all data values is 12 + 14 + 21 + 25 + 28 + 32 + 34 + 36 + 50 + 53 + 54 + 54 + 62 + 65 + 67 + 83 + 88 + 89 + 91 = 958

To find the mean, we have to divide the sum by the total number of values.

Mean = Sum of all data values ÷ 19 = 958 ÷ 19 = 50.42

iii) Range = the highest value - the lowest value = 91 - 12 = 79

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Practice Questions on Graphical Representation of Data

Faqs on graphical representation of data, what is graphical representation.

Graphical representation is a form of visually displaying data through various methods like graphs, diagrams, charts, and plots. It helps in sorting, visualizing, and presenting data in a clear manner through different types of graphs. Statistics mainly use graphical representation to show data.

What are the Different Types of Graphical Representation?

The different types of graphical representation of data are:

• Stem and leaf plot
• Scatter diagrams
• Frequency Distribution

Is the Graphical Representation of Numerical Data?

Yes, these graphical representations are numerical data that has been accumulated through various surveys and observations. The method of presenting these numerical data is called a chart. There are different kinds of charts such as a pie chart, bar graph, line graph, etc, that help in clearly showcasing the data.

What is the Use of Graphical Representation of Data?

Graphical representation of data is useful in clarifying, interpreting, and analyzing data plotting points and drawing line segments , surfaces, and other geometric forms or symbols.

What are the Ways to Represent Data?

Tables, charts, and graphs are all ways of representing data, and they can be used for two broad purposes. The first is to support the collection, organization, and analysis of data as part of the process of a scientific study.

What is the Objective of Graphical Representation of Data?

The main objective of representing data graphically is to display information visually that helps in understanding the information efficiently, clearly, and accurately. This is important to communicate the findings as well as analyze the data.

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Graphic Strategies for Analyzing and Interpreting Curricular Mapping Data

To describe curricular mapping strategies used in analyzing and interpreting curricular mapping data and present findings on how these strategies were used to facilitate curricular development.

Nova Southeastern University's doctor of pharmacy curriculum was mapped to the college's educational outcomes. The mapping process included development of educational outcomes followed by analysis of course material and semi-structured interviews with course faculty members. Data collected per course outcome included learning opportunities and assessment measures used.

Nearly 1,000 variables and 10,000 discrete rows of curricular data were collected. Graphic representations of curricular data were created using bar charts and stacked area graphs relating the learning opportunities to the educational outcomes. Graphs were used in the curricular evaluation and development processes to facilitate the identification of curricular holes, sequencing misalignments, learning opportunities, and assessment measures.

Mapping strategies that use graphic representations of curricular data serve as effective diagnostic and curricular development tools.

INTRODUCTION

Curricular evaluation and revision can be an intimidating process for educators. While most faculty members within a training program may feel that they understand what their curriculum should accomplish, it is often difficult to grasp what, how, and where specific content is addressed in the curriculum, or what measures are used to assess student achievement of curricular outcomes. Thus, when curricular revision is initiated, it can become a cumbersome and often confusing process for faculty members. Frequently, curricular decisions are based on faculty members' perceptions rather than from objective curricular data because these either are not available or are not interpreted easily. In these situations, curricular changes may be implemented that either are unnecessary or ineffective because a systematic curricular evaluation process has not been performed. Curricular mapping is emerging in higher education as the curricular evaluation tool that guides and makes the curricular evaluation and revision process more streamlined and transparent for stakeholders. 1 Curricular mapping has its roots in K-12 education, where it has been embraced as an effective curricular communication and decision-making tool within schools and across school districts. 2 - 4 In academic pharmacy, curricular mapping has become the state of the art curricular measurement tool, to the point that the process is a key criteria in Standard 12 of the Accreditation Council for Pharmacy Education (ACPE) Standards 2007. 5

Curricular mapping can be described simply as a technique that captures data about key curricular elements (content, outcomes, teaching and assessment strategies, etc.), and visually demonstrates the relationship among these elements so that curricular data can be interpreted and communicated more effectively. While curricular mapping is a systematic approach to curricular evaluation and revision, it is still a complex process that requires careful planning, assessment, and analysis. Higher education research literature offers several sources that outline different approaches to curricular mapping; 6 - 14 however, strategies for using curricular mapping data to its full potential has been defined less clearly.

In 2007, a team of faculty members at Nova Southeastern University (NSU) initiated a curricular mapping project which was completed in mid-2008. The mapping process is summarized briefly in this manuscript, yet the focus of this discussion is what happens after the collection of mapping data is complete. Readers who have participated in a curricular mapping project probably will agree that upon completion of a comprehensive curricular map, a massive set of data is left that can be overwhelming to analyze and interpret.

While completing mapping data collection requires extensive time and effort, that is only the halfway point. The next phase of curricular mapping is arguably the most important: analyzing those data and facilitating understanding of the curricular map among stakeholders. The purpose of this paper is to describe the curricular mapping strategies employed by Nova Southeastern University College of Pharmacy (NSU-COP) in analyzing and interpreting curricular mapping data and present findings on how these strategies are used to facilitate curricular development.

In mid-2007, NSU initiated its curricular mapping project. The goal of the project was to develop a curricular quality improvement tool to serve as the centerpiece for continuous curricular evaluation and improvement. In addition, the mapping tool would gather curricular data needed to meet ACPE 2007 Curriculum Standards 9-15. For the mapping tool to be useful, it needed not only to capture and organize curricular data, but more importantly, to allow the data to be presented in an easily visualized and interpreted manner.

The first phase of this project was to identify competency-based learning outcomes for the first professional doctor of pharmacy degree. Multiple sources were reviewed (Center for the Advancement of Pharmaceutical Education [CAPE] Outcomes, 2004 CAPE Supplemental Educational Outcomes offered by the American Association of Colleges of Pharmacy [AACP], the North American Pharmacist Licensure Examination [NAPLEX] blueprint, research literature, published outcomes from other programs similar to NSU, etc), and a preliminary list of learning outcomes was compiled. Each outcome on the list was then subjected to review to ensure that the outcome was action-based and measurable. The preliminary list of potential outcomes contained more than 1,400 items; the list was culled by rephrasing outcomes to eliminate overlap or redundancy. A list of approximately 400 outcomes was submitted to the NSU faculty for review. After 3 months of review, the faculty endorsed a list of 437 competency-based learning outcomes organized into 4 major domains (Table ​ (Table1 1 ).

Nova Southeastern University College of Pharmacy Educational Outcome Domain

There was concern that the college would need to design a new curriculum to achieve effective teaching of its outcomes. Rather than assume that such a radical change would be required, the college pursued the curricular mapping of the existing curriculum to guide curricular revision. The curricular mapping plan called for meeting with course coordinators to assess comprehensively how learning opportunities in their courses were aligned with the learning outcomes.

Next, the curricular mapping team defined key terms pertaining to mapping. Several classification schemes were defined a priori, such as the types of learning opportunities, the level of alignment between a learning opportunity and a learning outcome; the style of learning (active or passive) used to teach towards an outcome; the types of assessment measures corresponding to the outcome; the categories of the assessment to differentiate the content of assessment items; and the class of assessment (formative or summative). These definitions and codes are described in Appendix 1 . A semi-structured interview format was devised for faculty member interviews. Each session was conducted by 2 interviewers, who had reviewed all course materials prior to the interview. At the onset of the session, the faculty members were asked to describe their courses in detail. The interviewer then described the classification scheme and answered questions. Characteristics of the courses were also recorded, such as number of students enrolled, the training year/semester when the course was offered, the use of distance learning, the instructors involved in the course, etc.

The session involved moving through each outcome systematically and discussing how the course addressed that outcome. Due to the variation of teaching methods used throughout the curriculum, generating standard questions for each session was not possible, yet the probes were essentially:

• “Let's read the outcome. Does your course address that outcome in any way?”
• “At what level of alignment would you say the learning opportunities in your course support achievement of the outcome?”
• “What types of learning opportunities are used in your course to address that outcome?”
• “Do you use active learning to teach towards that outcome? If so, please describe those techniques.”
• “How do you assess that students have learned the material related to that outcome?”
• “What kinds of items do you include in that assessment?”
• “Do students receive feedback about their performance on the assessment? Do they have opportunities to remediate, if necessary?”

Sessions typically lasted about 2 hours, often because the interview generated much discussion. Faculty members enjoyed the opportunity to describe their teaching methods in this level of detail. Initial disagreements about classification were uncommon, and when they occurred, they were resolved unanimously through discussion. During the mapping sessions, the interviewers recorded faculty members' responses on standardized data collection sheets. These documents were later transferred into a database that was developed specifically for this project. The total time required to complete the mapping of a single course was about 3 hours. Data collection for the entire curriculum was completed in about 4 months.

EVALUATION AND ASSESSMENT

Upon completion of data collection, the curricular mapping database contained nearly 1,000 variables and approximately 10,000 discrete rows of data. The mapping team next confronted the formidable question: How can the mapping data be used optimally to answer key questions about the curriculum on an ongoing basis? To answer this question, the mapping team identified the visual format that would represent the mapping data best. A search of the literature revealed a variety of representations of mapping data that included topography maps, spreadsheet depictions, and checklists. 4 , 10 , 14 , 15 A simple, 1-dimensional map did not represent the curricular data in a way that was simple and user-friendly, therefore, multiple maps with different graphical representations were needed to illustrate visually the connections among curricular elements. To simply further the interpretation of curricular data by NSU curricular planners, the team generated solutions to the following set of key questions:

• (1) Are there outcomes that are not being taught in the current curriculum?
• (2) Are outcomes being taught in a sequential, progressive manner?
• (3) What learning opportunities are used in the curriculum? Are these passive or active?
• (4) What assessment measures are used in the curriculum? Are these formative or summative?

These questions are probably of interest to most, if not all, college curricular planners who undertake similar curricular mapping projects. The following presents how maps were used to address each of these questions.

(1) Are there outcomes that are not being taught in the current curriculum? Upon adopting learning outcomes, the college must ensure that its students are presented with opportunities to achieve those outcomes. NSU already had a curriculum in place and later adopted new competency-based learning outcomes, a different process than building a new curriculum according to a set of learning outcomes in which learning opportunities are created to address each outcome. The question became whether to jettison the existing curriculum and create an entirely new curriculum specifically designed to the new outcomes, or if revising the existing curriculum to allow for alignment to the new outcomes would be possible. This process involved matching the new outcomes to the learning opportunities of the current curriculum.

A significant component of this process was to search for curricular holes . A curricular hole is defined as an inconsistency between learning opportunities and learning outcomes, where no learning opportunity is provided for a given outcome. To assess for curricular holes, a graphical representation of the entire curricular map was created using a bar chart generated by SPSS (SPSS Inc, Chicago, IL). Figure ​ Figure1 1 presents the raw count of learning opportunities per outcome. The set of 437 outcomes has been condensed for space. The contours of the figure demonstrate that the NSU curriculum has emphasized curricular domains A (pharmaceutical care) and D (professionalism). Comparatively, domains B (systems management) and C (public health) have been emphasized less in the curriculum.

Analysis for Holes in Curriculum

An example of a curricular hole is represented by outcome statement A2.1.5, defined as design evidence-based disease management programs for populations. In all, 37 holes were found in the NSU curriculum. Because approximately 92% of the existing curriculum was found to match the new educational outcomes, an entirely new curriculum did not need to be created.

(2) Are outcomes being taught in a sequential, progressive manner? The NSU competency-based learning outcomes have been phrased as terminal outcomes ; these are tasks, activities, etc, that a student should be able to perform competently and autonomously at graduation (eg, “Assess patient adherence to prescribed medication regimens”). Students achieve outcomes through learning that is developmental and sequential. Outcome achievement typically requires that a student learns fundamental information, then learns how to think critically about that information, and ultimately implement that information in real-life environments. 16 An optimized curriculum should allow for such sequential learning. Because sequence gaps or inappropriate sequencing of learning opportunities for an outcome should not exist in the curriculum, the next analysis of curricular mapping data was exploring for the possibility of sequence gaps in the curriculum.

The NSU curricular mapping project designed a classification scheme that included levels of alignment among outcomes and learning opportunities. For most outcomes, the sequence should begin at alignment level 1 (background), then progress to level 2 (applied), and ultimately attain level 3 (practice). For example, if an outcome is taught only at level 3, skipping levels 1 and 2, a sequencing gap occurs. Another example of a sequencing gap is teaching an outcome at level 2 (applied) before level 1 (background). To identify sequence gaps in the overall curriculum, a stacked area graph was generated to represent the progression/development of curricular outcomes (Figure ​ (Figure2). 2 ). Several sequence gaps (labeled A-G in Figure ​ Figure2) 2 ) were identified in the NSU curriculum, as evidenced by a level of alignment in the overall curricular map being skipped (Figure ​ (Figure2 2 ).

Analysis for Sequence Gaps in Curriculum

Sequence gaps can be present in areas that appear to be properly sequenced at first glance (eg, Figure ​ Figure2, 2 , outcome area D1.1.5), but further exploration reveals a different pattern (eg, Figure ​ Figure3, 3 , outcomes D1.1.5, D1.1.5.1, and D1.1.5.2). To facilitate the efforts of curriculum planners, stacked bar graphs were developed to expose hidden sequence gaps (Figure ​ (Figure3 3 ).

Analysis for “Hidden Sequence Gaps” in Curriculum

Figure ​ Figure3 3 represents the learning opportunities provided to students in the curriculum for outcomes dealing with effective communication. Upon reviewing this map, 2 types of sequence gaps were exposed: those created due to a lack of learning opportunities in a given semester or year (eg, gaps A, B, and C in Figure ​ Figure3), 3 ), and those that occurred due to a learning opportunity level (eg, gaps D, E, and F in Figure ​ Figure3) 3 ) being skipped over consecutive semesters or years. While sequence gaps due to a lack of learning opportunities are easily identified, those due to a skipping of learning opportunity levels are more difficult to pinpoint. Gap D is a good example of a gap created due to a learning opportunity level being skipped. For outcome D1, learning opportunities are first introduced at level 1 (background), followed by level 3 (applied). However, learning opportunities at level 2 (practice) are skipped and never are provided for the outcome in the curriculum.

Figure ​ Figure3 3 shows that most of the learning opportunities for this set of outcomes were presented to students in the P2 and P4 years of the curriculum, while learning opportunities were either lacking in variety or numbers in the P1 and P3 years. Once hidden sequence gaps were identified, examining them in more detail to determine their cause was necessary.

Course level maps (Figure ​ (Figure4) 4 ) were then created to explore more effectively the location or cause of the sequence gaps identified in Figure ​ Figure3. 3 . The maps presented in Figure ​ Figure4 4 show how sequenced courses within a college department contributed to the development of the communication-related learning outcomes. These maps can be analyzed individually (course A, B, or C) to pinpoint the role of a given course in creating curricular sequence gaps, or in succession, as presented in Figure ​ Figure4, 4 , to show outcome development among courses. For example, Figure ​ Figure4 4 displays that course A provides few learning opportunities to address attaining communication-related outcomes, while course B provides substantially more opportunities, and course C provides opportunities for virtually all communication outcomes. Moreover, learning opportunities provided by these 3 courses are limited to the background and applied levels. The lack of learning opportunities for outcomes D1.1-D1.1.5.2 in course A (Figure ​ (Figure4) 4 ) contributes to the creation of gap A in Figure ​ Figure3. 3 . Furthermore, the lack of level 2 (applied) learning opportunities for outcomes D1 in course B (Figure ​ (Figure4) 4 ) may be responsible in part for creating gap D in Figure ​ Figure3. 3 . Analysis and interpretation of mapping data for the communication-related outcomes has led to a better understanding of how the curriculum handles these outcomes. The college has used these evidence-based strategies to guide curricular revision.

Between Course Sequence

(3) What learning opportunities are used in the curriculum? Are these passive or active? Learning opportunities represent a key area of the curriculum map. Identifying the learning opportunities used in a curriculum is important not only for facilitating curricular planners' understanding of how the curriculum is delivered, but also for meeting Standard 11 of the ACPE Accreditation Standards 2007. 5 Ideally, a variety of learning opportunities that provide for both passive and active student engagement should be employed, so that different student learning styles are accommodated, and developmental and sequential learning is supported. 17 NSU's mapping process collected data on the type, level, and style of learning opportunities ( Appendix 1 ). The learning opportunity levels were visualized using 2-dimensional area graphs (Figures ​ (Figures2 2 through ​ through4), 4 ), as described above.

Analysis of the learning opportunity type revealed that 8,810 learning opportunities were used in the NSU didactic and experiential core curriculum, and that these were delivered using 12 types of strategies (Table ​ (Table2). 2 ). The learning opportunities most often used were experiential education (31%), followed by lecture and discussion (29%), and lectures (19%). Overall, these 3 types of leaning opportunities accounted for 79% of strategies used in the curriculum.

Type of Learning Opportunities in Nova Southeastern University College of Pharmacy

In addition to understanding the type of learning opportunities, determining the style of learning opportunities used to gauge student engagement is also important. The style or nature of student engagement (ie, passive, active, or hybrid) that the learning opportunities offered in the didactic and introductory pharmacy practice experience (IPPE) curriculum was analyzed. Mapping determined that advanced pharmacy practice experiences (APPEs) were almost entirely based in active learning; therefore, APPEs were excluded from this analysis. Of the 5317 learning opportunities used in the didactic/IPPE curriculum, 34% were passive, or required little student engagement; 25% were active, requiring significant student participation and planned instruction; and 41% were hybrid. Hybrid learning opportunities were considered those that involved student interaction; however, the interaction was not planned by the instructor and was semi-structured. An example of a hybrid learning opportunity is a lecture and discussion session that includes informal discussion. Although some students may interact and fully engage in this type of learning opportunity, because it is not structured specifically to engage all students, others may not participate in the learning opportunity. Therefore, for some students the learning opportunity may be passive rather than active.

(4) What assessment measures are used in the curriculum? Are these formative or summative? Assessment and evaluation are essential components of a curriculum, allowing professors and students to gauge the acquisition of knowledge and skills towards educational outcomes. After all, providing a learning opportunity does not guarantee that students will learn the material. Assessment processes provide data about the effectiveness of learning opportunities.

Because assessment is such a pivotal and significant component of professional training, it naturally goes hand-in-hand with curricular planning. Consequently, the curricular mapping process integrated the collection of different assessment techniques used by faculty members. Yet for the purposes of curricular planning, data about assessment techniques were found presented best in aggregate.

The assessment components of the curriculum map identify the range of assessment techniques used in the curriculum. The expectation was that the college should deploy a variety of assessment strategies which should include both formative and summative measures in assessing student achievement of learning outcomes. As with the learning opportunities, NSU's mapping process linked the assessment measures to the learning outcomes and classified these by type, category, and class ( Appendix 1 ).

In all, 5,317 assessment measures were used throughout the didactic and IPPE curriculum to assess student performance, indicating that professors routinely integrated assessment into their courses. Table ​ Table3 3 provides a breakdown of the 12 types of assessment strategies that were used. Quizzes (53%) were the most commonly used assessment measure, followed by written assignments (10%), and written examinations (8%). Not surprising, quizzes were used most, as this type of assessment generally is easier to develop and administer and can be used to assess diverse learning opportunities in a variety of settings. Interestingly, 10% of assessment opportunities were classified by faculty members as informal (not formally assessed). This describes the case when a professor provides a learning opportunity towards 1 or more of the educational outcomes, yet uses intuition to gauge whether the material was understood by students. For example, a professor may present new material and notice that many students seem confused; a formal assessment is not needed in this case to inform the skilled educator to cover the new material further.

Type of Assessment Measure

Most of the 5,317 assessment strategies utilized were summative (54%) in nature. A large proportion of formative assessment measures may be desirable because they provide the information needed to adjust teaching and learning in progress.

Assessment for curricular holes is an important part of the curricular evaluation and development process. Once holes are identified, their causes must be determined, and strategies must be developed to address them. In general, curricular holes, such as one presented in Figure ​ Figure1, 1 , can be caused either by a deficiency in the curriculum to provide the learning opportunity, or the lack of fit of the outcome to the goal of the curriculum. Curricular planners can use at least 3 possible strategies to address curricular holes: teaching opportunities may be created to address attaining the outcome, the outcome may be revised to better fit the goal of the curriculum, or the outcome may be dropped altogether if it is deemed inconsistent with the goal of the curriculum. Through the curricular revision process, the college continues to address how best to eliminate the identified holes.

Curricular mapping using stacked graphs (Figures ​ (Figures2 2 through ​ through4) 4 ) has yielded data used to drive interpretations and continuous discussions about curricular sequencing and alignment. In addition to answering basic questions about progression of outcomes in the curriculum and among courses, stacked graphs, as presented in Figure ​ Figure4, 4 , can help address other course sequencing questions such as: Are course prerequisites appropriate? How should the level of learning opportunities be sequenced among courses to meet the educational outcome effectively? For example, for outcomes D1.1 and D1.1.1 (Figure ​ (Figure4) 4 ) an instructor in course C may assume that students have received learning opportunities in courses A and B at level 1 (background) before they are presented in course C at level 2 (applied). However, the graph shows that this is not the case. In fact, students are provided with learning opportunities for these 2 outcomes for the first time in course C. Adjustment of learning opportunities (ie, changing prerequisites) in courses A and B would be required to ensure that students are prepared for course C. Alternatively, course C could be changed to provide learning opportunities at level 1 (background) before level 2 (applied) learning opportunities are introduced.

Outcomes D1.1.2 and D1.1.3 in courses B and C of Figure ​ Figure4 4 provide a good example of the way that learning opportunity levels should build on each other from course to course. Course B, offered in the fall semester of the P2 year, presents learning opportunities at level 1 (background) while course C, offered in the winter semester of the P2 year, presents learning opportunities at level 2 (practice). Learning opportunities in these 2 courses build upon each other progressively without skipping levels. The use of stacked course graphs in this manner aids curricular planners in developing strategies to ensure consistent outcome development among courses in the curriculum.

Figures ​ Figures2 2 through ​ through4 4 also have generated discussion about redundancy or duplication in the curriculum. A cursory glance at the maps might suggest that there are outcomes that are being taught to students repetitively throughout the curriculum. However, multiple teaching efforts towards the same outcome may have significant benefits to the student. The outcome may be taught using different techniques, contexts, perspectives, assessment methods, etc. Further, overlap/redundancy in teaching may reflect the importance of the outcome itself. Notably, input from students regarding this curricular mapping issue was unequivocal: students value having core material presented to them repeatedly throughout their training. However, the issue of curricular overlap/redundancy merits attention for at least 2 reasons. First, a saturation point may exist beyond which further teaching towards the outcome is unnecessary or ineffective. By identifying and removing true cases of redundancy that have no significant educational merit, the curriculum can be streamlined and allow holes and sequence gaps in the curriculum to be filled. Second, conflicting information pertaining to the same outcome also may be presented to students. For example, professors X and Y may teach to the same outcome in their respective courses, yet present students with contradictory information. Similarly, because these professors may not realize they are teaching towards the same outcome, they should collaborate to ensure student success. Maps similar to those used to detect curricular gaps (Figure ​ (Figure3 3 and ​ and4) 4 ) can be generated to identify and explore curricular redundancies. Analysis for curricular redundancies would center on identifying repetitive presentation of learning opportunities (count and level) for individual outcomes over the course of the curriculum, rather than searching for omissions or skipping of learning opportunity levels as with sequence gaps.

The form of analysis and interpretation of sequence gaps and redundancies presented has led to a better understanding of how outcomes are addressed in the overall curriculum and among related courses. The outcomes presented here are but one area of the curriculum. The college continues to review all outcomes using this systematic process to identify all significant sequence gaps and possible redundancies. Continuous mapping will be used to ensure that planned curricular revisions are consistent with the delivered curriculum.

The authors did not expect to detect such diversity in the type of learning opportunities that were used throughout the curriculum. The range of learning opportunities was also contrary to the perception of most faculty members who believed that a limited number were in place. Also surprising was the finding that 66% of student learning experiences involved either active or hybrid learning. These findings have generated new discussions among faculty members. A further unexpected byproduct of the mapping process has been the more widespread sharing of active-learning techniques. Curricular maps have also been used by the college to propose that small group activities be offered more often and take on greater emphasis as a learning opportunity.

Typically, assessment techniques are determined by the professor(s) coordinating the course and are not directly under the supervision of a curriculum committee. Our findings have generated discussion among faculty members about the use of assessment techniques across courses, and the potential has been indicated for more detailed mapping analyses to determine how to best deploy assessment measures in the curriculum. The assessment data collected through curricular mapping are being used within the curricular revision process to coordinate the use of assessment strategies in the revised curriculum.

In the final analysis of the NSU curriculum, the current curriculum was determined to be well aligned to the competency-based learning outcomes. The faculty members agreed that revisions to the curriculum were warranted, but it was not deemed necessary to abandon the existing curriculum and create an entirely new one. Areas in need of revision were specific, and therefore the revision process would be direct with clearly recognized goals. The curricular mapping process served as an effective diagnostic and curricular development tool. Further curricular development will focus upon answering other important questions with the help of mapping data. The next step for the NSU mapping program is to analyze assessment data with the same level of specificity as the curricular outcomes, with the hope of refining assessment techniques across the curriculum.

Curricular mapping is becoming a common method used for curricular evaluation. Curricular mapping demonstrates the relationship among components of the curriculum to facilitate stakeholder understanding of curriculum delivery. However, this process can be difficult if the data collected are not presented in ways that are easily understood. A variety of formats can be used to represent complex curricular mapping data visually to facilitate understanding. Maps can be created to show deficiencies or holes, gaps or misalignments, and unnecessary redundancies in the curriculum. Additionally, mapping can be used to evaluate how learning opportunities and assessment measures are applied. Curricular data depicted in this fashion helps curricular planners better interpret the information gathered and facilitates the curricular development process. To be clear, there is no single “right” or “best” way to visually present mapping data. The authors' hope is that by sharing one college's approach, others may be inspired to build upon and improve the methods presented here.

Appendix 1. Classification Scheme for Nova Southeastern University College of Pharmacy Curricular Mapping Project

• Math Article

Graphical Representation

Graphical Representation is a way of analysing numerical data. It exhibits the relation between data, ideas, information and concepts in a diagram. It is easy to understand and it is one of the most important learning strategies. It always depends on the type of information in a particular domain. There are different types of graphical representation. Some of them are as follows:

• Line Graphs – Line graph or the linear graph is used to display the continuous data and it is useful for predicting future events over time.
• Bar Graphs – Bar Graph is used to display the category of data and it compares the data using solid bars to represent the quantities.
• Histograms – The graph that uses bars to represent the frequency of numerical data that are organised into intervals. Since all the intervals are equal and continuous, all the bars have the same width.
• Line Plot – It shows the frequency of data on a given number line. ‘ x ‘ is placed above a number line each time when that data occurs again.
• Frequency Table – The table shows the number of pieces of data that falls within the given interval.
• Circle Graph – Also known as the pie chart that shows the relationships of the parts of the whole. The circle is considered with 100% and the categories occupied is represented with that specific percentage like 15%, 56%, etc.
• Stem and Leaf Plot – In the stem and leaf plot, the data are organised from least value to the greatest value. The digits of the least place values from the leaves and the next place value digit forms the stems.
• Box and Whisker Plot – The plot diagram summarises the data by dividing into four parts. Box and whisker show the range (spread) and the middle ( median) of the data.

General Rules for Graphical Representation of Data

There are certain rules to effectively present the information in the graphical representation. They are:

• Suitable Title: Make sure that the appropriate title is given to the graph which indicates the subject of the presentation.
• Measurement Unit: Mention the measurement unit in the graph.
• Proper Scale: To represent the data in an accurate manner, choose a proper scale.
• Index: Index the appropriate colours, shades, lines, design in the graphs for better understanding.
• Data Sources: Include the source of information wherever it is necessary at the bottom of the graph.
• Keep it Simple: Construct a graph in an easy way that everyone can understand.
• Neat: Choose the correct size, fonts, colours etc in such a way that the graph should be a visual aid for the presentation of information.

Graphical Representation in Maths

In Mathematics, a graph is defined as a chart with statistical data, which are represented in the form of curves or lines drawn across the coordinate point plotted on its surface. It helps to study the relationship between two variables where it helps to measure the change in the variable amount with respect to another variable within a given interval of time. It helps to study the series distribution and frequency distribution for a given problem.  There are two types of graphs to visually depict the information. They are:

• Time Series Graphs – Example: Line Graph
• Frequency Distribution Graphs – Example: Frequency Polygon Graph

Principles of Graphical Representation

Algebraic principles are applied to all types of graphical representation of data. In graphs, it is represented using two lines called coordinate axes. The horizontal axis is denoted as the x-axis and the vertical axis is denoted as the y-axis. The point at which two lines intersect is called an origin ‘O’. Consider x-axis, the distance from the origin to the right side will take a positive value and the distance from the origin to the left side will take a negative value. Similarly, for the y-axis, the points above the origin will take a positive value, and the points below the origin will a negative value.

Generally, the frequency distribution is represented in four methods, namely

• Smoothed frequency graph
• Pie diagram
• Cumulative or ogive frequency graph
• Frequency Polygon

Merits of Using Graphs

Some of the merits of using graphs are as follows:

• The graph is easily understood by everyone without any prior knowledge.
• It saves time
• It allows us to relate and compare the data for different time periods
• It is used in statistics to determine the mean, median and mode for different data, as well as in the interpolation and the extrapolation of data.

Example for Frequency polygonGraph

Here are the steps to follow to find the frequency distribution of a frequency polygon and it is represented in a graphical way.

• Obtain the frequency distribution and find the midpoints of each class interval.
• Represent the midpoints along x-axis and frequencies along the y-axis.
• Plot the points corresponding to the frequency at each midpoint.
• Join these points, using lines in order.
• To complete the polygon, join the point at each end immediately to the lower or higher class marks on the x-axis.

Draw the frequency polygon for the following data

Mark the class interval along x-axis and frequencies along the y-axis.

Let assume that class interval 0-10 with frequency zero and 90-100 with frequency zero.

Now calculate the midpoint of the class interval.

Using the midpoint and the frequency value from the above table, plot the points A (5, 0), B (15, 4), C (25, 6), D (35, 8), E (45, 10), F (55, 12), G (65, 14), H (75, 7), I (85, 5) and J (95, 0).

To obtain the frequency polygon ABCDEFGHIJ, draw the line segments AB, BC, CD, DE, EF, FG, GH, HI, IJ, and connect all the points.

Frequently Asked Questions

What are the different types of graphical representation.

Some of the various types of graphical representation include:

• Line Graphs
• Frequency Table
• Circle Graph, etc.

Read More:  Types of Graphs

What are the Advantages of Graphical Method?

Some of the advantages of graphical representation are:

• It makes data more easily understandable.
• It saves time.
• It makes the comparison of data more efficient.

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Very useful for understand the basic concepts in simple and easy way. Its very useful to all students whether they are school students or college sudents

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Fully-Connected Spatial-Temporal Graph for Multivariate Time-Series Data

• Yucheng Wang Institute for Infocomm Research, A*STAR Nanyang Technological University
• Yuecong Xu Institute for Infocomm Research, A*STAR
• Jianfei Yang Nanyang Technological University
• Min Wu Institute for Infocomm Research, A*STAR
• Xiaoli Li Institute for Infocomm Research, A*STAR Nanyang Technological University Centre for Frontier AI Research, A*STAR
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Computer Science > Computer Vision and Pattern Recognition

Title: sg-pgm: partial graph matching network with semantic geometric fusion for 3d scene graph alignment and its downstream tasks.

Abstract: Scene graphs have been recently introduced into 3D spatial understanding as a comprehensive representation of the scene. The alignment between 3D scene graphs is the first step of many downstream tasks such as scene graph aided point cloud registration, mosaicking, overlap checking, and robot navigation. In this work, we treat 3D scene graph alignment as a partial graph-matching problem and propose to solve it with a graph neural network. We reuse the geometric features learned by a point cloud registration method and associate the clustered point-level geometric features with the node-level semantic feature via our designed feature fusion module. Partial matching is enabled by using a learnable method to select the top-k similar node pairs. Subsequent downstream tasks such as point cloud registration are achieved by running a pre-trained registration network within the matched regions. We further propose a point-matching rescoring method, that uses the node-wise alignment of the 3D scene graph to reweight the matching candidates from a pre-trained point cloud registration method. It reduces the false point correspondences estimated especially in low-overlapping cases. Experiments show that our method improves the alignment accuracy by 10~20% in low-overlap and random transformation scenarios and outperforms the existing work in multiple downstream tasks.

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