Notes on Statistics Education(loosely based on C. Franklin's ppt at the ASA website)

• Curriculum Standards (PSSM) of the National Council of Teachers of Mathematics (NCTM)

• One of the 5 strands, Data Analysis and Probability, runs throughout the curriculum, from Pre-K to grade 12…

Data Analysis & Probability Strand

Instructional programs from Pre-K through grade 12 should enable all students to—

• formulate questions that can be addressed with data and

• collect, organize, and display relevant data to answer them;

• select and use appropriate statistical methods to analyze data;

• develop and evaluate inferences and predictions that are based on data;

• understand and apply basic concepts of probability.

Statistics and Data Analysis – PCAI

Process of Statistical

Investigation

Pose the question(s)

Collect the data

Interpret the results

Analyze the distribution(s)

• Many teachers have not had any opportunity to develop sound knowledge of the principles and practices of statistics, data analysis, and probability they are now called upon to teach

• The GAISE report helps by giving a structure to teaching this strand in K-12: – Guidelines for Assessment and Instruction in Statistics

Education– The main content of the K-12 Framework is divided

into three levels, A, B, and C that parallel the PreK-5, 6-8, and 9-12 grade bands of the NCTM Standards, but these levels are based on experience not age.

GAISE (Franklin)

The foundation for the K-12 Framework rests on the NCTM Standards.

• This Framework fleshes out the NCTM Data Analysis and Probability strand with guidance and clarity on the content that NCTM is recommending at the elementary, middle and high school grades, focusing on a connected curriculum that will allow a high school graduate to have a working knowledge of an appreciation for the basic ideas of statistics.

• It also provides guidance on methods that are accepted as effective in teaching statistical concepts to students with wide varieties of learning styles.

3 levels of learning in the GAISE report

• At Level A the learning is more teacher driven, but transitions toward student centered work at Level B and becomes highly student driven at Level C. Hands-on, active learning is a predominant feature throughout.

Distinction of Levels

• All four steps of the PCAI process are applied at all three levels, but the depth of understanding and sophistication of methods used increases across the levels.

• One example of these is Graph Comprehension– reading the data– reading between the data– reading beyond the data

Distinction of Levels

• Level A: Reading the data: a literal reading of the graph - "lift" the facts that are explicitly seen on the graph - no interpretation

• Level B: Reading between the data: includes interpretation, requires ability to compare and identify mathematical relationships in the graph

• Level C: Reading beyond the data: make inferences or predictions from the graph that are not explicitly stated in the data; requires integration of many areas of conceptual understandings

Distinction of LevelsAnother example of clarity of concepts at each level:• What type of music is most popular among their

peers in school? (rock, country, rap)• Level A: Summarize frequencies in table or bar

graph• Level B: Transition to relative frequencies – leap to

proportional reasoning• Level C: Transition to sampling distributions for a

sample proportion and role of probability in finding a margin of error which provides information about max. likely distance between sample proportion and population proportion being estimated.

To summarize…

Basic principles around which the Framework revolves can be summarized as:

• Both conceptual understanding and procedural skill should be developed deliberately, but conceptual understanding should not be sacrificed for procedural proficiency.

• Active learning is key to the development of conceptual understanding.

• Real world data must be used wherever possible in statistics education.

• Appropriate technology is essential in order to emphasize concepts over calculations… and this leads us to Tinkerplots!

• Open TinkerPlots & note the empty window…• PCAI: Questions? Collect Data… Analyze… Interpret.

In classes, collect your own data:– drag down either the Cards or Table icon, add a New attribute

(or more) and then type in your own data…

• … or use built-in TinkerPlots datasets (File… Open…)• … Copy and Paste (from a file - go to my website, STT

215 Honors, open the Lean Body Mass file (note .csv), copy, paste into an open Cards icon). Let's work with this TinkerPlots dataset for a few minutes to recall some of the basics of the program…

• Import from File (this works for text files only) • Import from URL (go to my website, copy link location

of the CO2 data, paste…)• Once the data is in a dataset, notice that it is in the form

of cases (rows, observations) and attributes (columns, variables) -

• PCAI: Questions? Collect Data… Analyze… Interpret. Graphics can be created by organizing the icons in the plot window; so work with the Lean Body Mass dataset…colors, categorical plots, icon types, fuse into bar graph; then quantitative variable, line plot (stack), dividers, averages, histogram, order vertically, drawing tool for boxplot,…

• Open the TinkerPlots file: Heaviest Backpacks.tp – look at the lesson plan for this dataset, backpack_lesson.pdf and notice

the questions that are asked throughout (PCAI)– do kids in the higher grades carry heavier backpacks?– what about boys and girls? a difference in their backpack weights?– what about the 15% of body weight cutoff recommended by doctors?

• Look at the next slide to see various parts of a plot… then try various plots to help lead you to answers of the questions posed above…some additional questions are given below…– can you make a value bar graph showing the pack weights labeled by the

students names, ordered by the backpack weights? colored by the variable grade? now a regular line plot of backpack weights, colored by grade? put these one above the other and compare … note how to get the line plot from the value bar graph.

– can you make a bar graph showing the frequency distribution of the categorical variable grade? color the bars with the backpack weights?

QuickTime™ and a decompressor

are needed to see this picture.

Can you make a plot similar to this one to answer the question about backpack weights in the different grades? Notice the labels for the icons with the childrens' names and the colors correspond to the grade level, and the bars are ordered by backpack weights… this is a value bar graph. A line plot?

Backpack

SadieMaddynAbigailEugene

RossWesley

CameronChad

AngieEmma

JimIsableRiley

DanLeroyFinley

JacksonRachel

ErinBryantWendie

DeborahBaileyMicah

KayleenTrevor

AnthonyDarrylLorien

EllyHaley

AlysaaKarsten

GregJoshTodd

ByronChessaNathan

KristenWendyLarryMegan

MichaelMattLenn

SherryTim

KilieBrennanBrandyAlisonQuinnChris

HeatherBradLori

KellyMimiRyan

JenniferTanner

KenWarrenDarice

MerindaPat

AlanPaulPhil

MyrleKeithKatie

SteveWilliam

TysonKathy

JeffreyGayle

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40

PackWeight (lb)

GradeFiveOneSevenThree

Value Bar Horizontal

Here's what your formula window should look like when you're creating the new attribute pctwt…

• Now let's try out the PCAI method on our signatures… look at the lesson (part #1) on measuring the lengths of our signatures and complete the first two pages…– what are the questions that occur to you about dominant and

non-dominant signatures after doing this data collection activity?– can you use the TinkerPlots skills you learned this morning to

answer those questions? – write up your results in a TinkerPlots document using the Text

boxes, justifying your conclusions with graphics and statistics!

• Now look at part #2 of the Signatures lesson - I anticipate these questions will keep us busy with TinkerPlots for the remainder of the time!