Textbook Coding

Background:

Six textbook series, CME, CPMP, Disc, Glencoe, IMP, and UCSMP have been examined, scoring each and every question for the mathematical concepts involved as well as the "Cognitive Behavior" required to address the question in the context in which it appears in the textbook. A total of 63,174 questions have been scored across all series and a total of 86,895 topic codes assigned. Each question was evaluated by two people who met and discussed any discrepancies in their assessments. Results reported here are based on their reconciled scorings.

Discussion and images below may not reflect the most recent versions available. Check the dates of the attachments, typically the most up-to-date output will be found in Compressed Zip archive seriesTextbooks.zip.

All PDF pdf output files are vector graphs which can be zoomed to see more detail.

Table of Contents

Consolidation!

  • :ods: seriesData.ods: Spreadsheet with Reconciled data from All series: CME, CPMP, Disc, Glencoe, IMP, UCSMP; each in a separate sheet.

Analysis Resources

  • Compressed Zip archive seriesTextbooks.zip: download and unzip this zip file to find:
    • HTML index.html html output of the primary Mathematica Notebook used for processing. The index.html page has supporting folders HTMLFiles and HTMLLinks . Note: many of the images provide further details when your cursor hovers over various portions of the image. e.g. Actual underlying counts in the pie charts.
    • PNG png and PDF pdf complete set of output files. All PDF files are scalable vector graphics and text so you can zoom in for details and out for the overview.
  • Files below are representative, but are unlikely to be as up-to-date as in the zip file above.
  • :nb: seriesTextbooks.nb: seriesTextbooks Mathematica Notebook. This file contains no output. To run, place in folder with:
    • :ods: seriesData.ods: Spreadsheet with Reconciled data from All series: CME, CPMP, Disc, Glencoe, IMP, UCSMP; each in a separate sheet.
    • :ods: seriesContext.ods: Spreadsheet with context information along with valid codes and various "handles" for them.

Cognitive Behavior

These Pie Charts provide an overall summary of the three types of Cognitive Behavior: Knowing, Applying, and Reasoning.

CogBeh_PieChart.png

The graph below, based on the idea of a Ternary Plot or Composition Plot, provides another way to summarize the three types of Cognitive Behavior: Knowing, Applying, and Reasoning. This presentation:

  • Shows the Pie charts given above as well as a chart for each textbook in the series.
  • Scales each pie chart acording to the number of questions represented
  • Positions each pie chart in a way that makes visual comparisons much more accessible.
The three corners of the plot represent each of the Cognitive Behaviors: Knowing, Applying, and Reasoning. Each corner of the triangle represents 100% for that feature. The side of the triangle opposite each corner represents 0% and spreads the remaining two features along it. To help characterize the triangle in terms of the more familiar pie charts, a background of small pie charts shows the underlying "Landscape" of how the large triangle portrays the proportions. It also helps you to read off approximate values for a position in the chart since there is a row for each 10% change in proportion. There is also a small pie chart in the center of the large triangle, locating equal proportions for all three features. Each textbook series is represented in the plot by a pie chart with its position representing all texts within the series as well as a pie chart for each of the (up to three) volumes in the series, represented by .1, .2, .3 in the label.

Beneath the graphic is a narrative highlighting some observations which this presentation makes particularly accessible:

TernaryPlotPies.png

From the plot, showing 17 pie charts, their location on the plot shows, for example, that CPMP consistently involves more reasoning and that the "orbit" of the series starts with a comparative emphasis on reasoning, shifting towards knowing in year 2 and then moving to applying in year 3. Glencoe and UCSMP have very little reasoning and move from knowing to applying from book 1 to book 2. CME, in contrast, moves away from applying and knowing towards more reasoning in going from year 1 to year two. The central white tirangle represents compositions with no clear majority. Each colored triangle indicates majority representation of the associated Cognitive Behavior. All textbooks in all series lie in the top triangle, indicating that they devote more than half of their questions to Applying.

Content

Content_PieChart.png Content_Legend_PieChart.png

Other Aspects

Other_BarChart.png

Timeline Graphs

CME Algebra 1&2 [CME]

CME_Timeline_Graph.png

Core Plus Mathematics Program [CPMP]

CPMP_Timeline_Graph.png

Discovering (Advanced) Algebra [Disc]

Disc_Timeline_Graph.png

Glencoe Algebra 1 & 2 [Glencoe]

GA12_Timeline_Graph.png

Interactive Mathematics Program [IMP]

IMP_Timeline_Graph.png

University of Chicago School Mathematics Project [UCSMP]

UCSMP_Timeline_Graph.png


-- DickFurnas - 2009-09-18

Attachments

Topic attachments
I Attachment History Action Size Date Who Comment
PDFpdf CME_Timeline_Graph.pdf r3 r2 r1 manage 1732.8 K 2015-07-14 - 16:39 DickFurnas Harmonized to 2015-07-14
PNGpng CME_Timeline_Graph.png r4 r3 r2 r1 manage 150.8 K 2015-07-14 - 16:40 DickFurnas Harmonized to 2015-07-14
PDFpdf CPMP_Timeline_Graph.pdf r6 r5 r4 r3 r2 manage 1150.4 K 2015-07-14 - 16:41 DickFurnas Harmonized to 2015-07-14
PNGpng CPMP_Timeline_Graph.png r6 r5 r4 r3 r2 manage 167.5 K 2015-07-14 - 16:41 DickFurnas Harmonized to 2015-07-14
PDFpdf CogBeh_PieChart.pdf r10 r9 r8 r7 r6 manage 16.5 K 2015-07-15 - 06:50 DickFurnas Harmonized to 2015-07-15 [Disc]
PNGpng CogBeh_PieChart.png r10 r9 r8 r7 r6 manage 51.9 K 2015-07-15 - 06:52 DickFurnas Harmonized to 2015-07-15 [Disc]
PDFpdf Content_Legend_PieChart.pdf r14 r13 r12 r11 r10 manage 32.7 K 2015-07-14 - 16:43 DickFurnas Harmonized to 2015-07-14
PNGpng Content_Legend_PieChart.png r13 r12 r11 r10 r9 manage 106.2 K 2015-07-14 - 16:44 DickFurnas Harmonized to 2015-07-14
PDFpdf Content_PieChart.pdf r11 r10 r9 r8 r7 manage 18.5 K 2015-07-15 - 06:53 DickFurnas Harmonized to 2015-07-15 [Disc]
PNGpng Content_PieChart.png r13 r12 r11 r10 r9 manage 107.3 K 2015-07-15 - 06:59 DickFurnas Harmonized to 2015-07-15 [Disc]
PDFpdf Disc_Timeline_Graph.pdf r1 manage 1541.7 K 2015-07-15 - 06:49 DickFurnas New name for Series [Disc] rather than [DA]
PNGpng Disc_Timeline_Graph.png r1 manage 185.7 K 2015-07-15 - 06:48 DickFurnas New Name for series [Disc]
PDFpdf Glencoe_Timeline_Graph.pdf r4 r3 r2 r1 manage 2122.3 K 2015-07-14 - 16:49 DickFurnas Harmonized to 2015-07-14
PNGpng Glencoe_Timeline_Graph.png r4 r3 r2 r1 manage 168.0 K 2015-07-14 - 16:49 DickFurnas Harmonized to 2015-07-14
PDFpdf IMP_Timeline_Graph.pdf r6 r5 r4 r3 r2 manage 298.3 K 2015-07-14 - 16:50 DickFurnas Harmonized to 2015-07-14
PNGpng IMP_Timeline_Graph.png r7 r6 r5 r4 r3 manage 114.2 K 2015-07-14 - 16:50 DickFurnas Harmonized to 2015-07-14
PDFpdf Other_BarChart.pdf r9 r8 r7 r6 r5 manage 28.6 K 2015-07-15 - 06:54 DickFurnas Harmonized to 2015-07-15 [Disc]
PNGpng Other_BarChart.png r9 r8 r7 r6 r5 manage 63.7 K 2015-07-15 - 06:54 DickFurnas Harmonized to 2015-07-15 [Disc]
PNGpng TernaryPlotPies.png r3 r2 r1 manage 75.9 K 2014-02-12 - 16:56 DickFurnas  
PDFpdf UCSMP_Timeline_Graph.pdf r6 r5 r4 r3 r2 manage 1657.8 K 2015-07-14 - 16:52 DickFurnas Harmonized to 2015-07-14
PNGpng UCSMP_Timeline_Graph.png r7 r6 r5 r4 r3 manage 189.4 K 2015-07-14 - 16:52 DickFurnas Harmonized to 2015-07-14
Unknown file formatods seriesContext.ods r1 manage 72.5 K 2015-07-14 - 16:00 DickFurnas The seriesContext.ods file contains context information along with valid codes and various "handles" for them.
Unknown file formatods seriesData.ods r13 r12 r11 r10 r9 manage 2308.9 K 2015-07-15 - 06:32 DickFurnas The primary data file with all codings. Now includes a sixth series, Discovering (Advanced) Algebra [Disc]
Unknown file formatnb seriesTextbooks.nb r3 r2 r1 manage 162.1 K 2015-07-15 - 07:07 DickFurnas The Mathematica Notebook used to analyze the seriesTextbooks.ods data file. This notebook contains no output. Place in folder with seriesData.ods and seriesContext.ods to run.
Compressed Zip archivezip seriesTextbooks.zip r15 r14 r13 r12 r11 manage 11477.8 K 2015-07-15 - 07:07 DickFurnas zip file of Mathematica notebook output folder. Includes pdf files and html rendition of the notebook

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Topic revision: r38 - 2015-07-20 - DickFurnas
 
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