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Week 3

Analyze the Learning Tasks

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Last week’s questions

Can problems be the same for I-PS and PS-I ?

Yes, but they don’t have to be same. Make it easy enough to compare if they are close

Do we have to do I-PS vs PS-I ?

We suggest doing so, but not necessary (do PS-I if you have only one condition)

Sample size? Time?

Best you can do. ~40 ideally. It doesn’t hurt grade if you don’t meet that number
Time: tradeoff between you finding participants and students learning something

How scaffolded should it be? Isn’t it frustrating? What’s a good problem ?

Participants are not meant to directly learn in the PS activity. It's used as a preparation for learning, by activating students' prior knowledge, making them aware of their knowledge gap and making them eager to learn more
For this reason, a good PS activity should have some properties: hard, open-ended and/or several paths to reach a solution, multiple representation, etc.

Assessment? Learning goals?

…

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Project Goal: Create Two Versions of a Learning Experience and Compare Them Experimentally

Info & Consent

Pretest

Open-Ended Problem Solving

Instruction

Problem Solving

Posttest

PS-I Condition

N=20

I-PS Condition

N=20

10 mins

5 mins

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Designing “Good” Problems

Info & Consent

Pretest

Open-Ended Problem Solving

Instruction

Problem Solving

Posttest

PS-I Condition

N=20

I-PS Condition

N=20

10 mins

5 mins

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Learning Goals and Assessment

Info & Consent

Pretest

Open-Ended Problem Solving

Instruction

Problem Solving

Posttest

PS-I Condition

N=20

I-PS Condition

N=20

10 mins

5 mins

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Backward Design

Topic

Learning Goals

What should students be able to do?

Assessment How will they show they can do it?

Learning Experience What activities will students learn from?

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Backward Design

Topic

Learning Goals

What should students be able to do?

Assessment How will they show they can do it?

Learning Experience What activities will students learn from?

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Learning Goals

Articulate the things a student should be able to do at the end of the lesson
The learning objectives should be specific
The learning objectives should use action verbs

Apply, state, prove, decide, explain, describe

The learning objectives should be measurable

Not just say “understand”, but how do they show this understanding

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Action Verbs to Describe Learning Objectives

List, Memorize, Relate, Identify, Show, Locate, Reproduce, Quote, Repeat, Label, Group, Read, Write, Outline, Choose, Recite, Match, Cite, Define
Restate, Discuss, Translate, Give examples of, Paraphrase, Reorganize, Describe, Outline, Account for, Interpret, Explain
Exhibit, Illustrate, Calculate, Make, Apply, Operate, Change, Compute, Sequence, Solve, Demonstrate, Use, Adapt, Predict
Ascertain, Diagnose, Distinguish, Analyze, Examine, Conclude, Infer
Appraise, Critique, Decide, Judge, Compare, Contrast, Deduce, Weigh, Evaluate
Combine, Devise, Expand, Plan, Compose, Extend, Create, Design, Invent, Develop, Modify

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Backward Design

Topic

Learning Goals

What should students be able to do?

Assessment How will they show they can do it?

Learning Experience What activities will students learn from?

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Assessment Questions

You should be able to explain what type of knowledge each of your assessment questions evaluates
You should be able to explain how students will learn this knowledge during your learning experience
Your assessment questions should be clearly related to your learning goals and to your knowledge to-be-learned

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Backward Design

Topic

Learning Goals

What should students be able to do?

Assessment How will they show they can do it?

Learning Experience What activities will students learn from?

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Learning Experience

Info & Consent

Pretest

Open-Ended Problem Solving

Instruction

Problem Solving

Posttest

PS-I Condition

N=20

I-PS Condition

N=20

10 mins

5 mins

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Learning Experience

For PS-I, students learn from I but not PS.

They do NOT need to solve the problem!

Schwartz, D. L., & Martin, T. (2004). Inventing to prepare for future learning: The hidden efficiency of encouraging original student production in statistics instruction. Cognition and instruction, 22(2), 129-184.

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Learning Experience

For PS-I, students learn from I but not PS.

They do NOT need to solve the problem!

➡ “Complex enough” and “open-ended”

Schwartz, D. L., & Martin, T. (2004). Inventing to prepare for future learning: The hidden efficiency of encouraging original student production in statistics instruction. Cognition and instruction, 22(2), 129-184.

This study was for ninth-grade students��Six common ways students computed reliability:

(A) Find the area covered by the pitches—equivalent to a range formula, because only the far points affect the answer.

(B) Find the perimeter using the Pythagorean theorem to compute each line segment—similar to summing the distances between consecutive numbers in a data list, except it often ignores interior points.

(C) Find the average distances between pairs of points—though pairings are haphazard, it uses the average instead of summing.

(D) Find average distance from an arbitrary starting point to all other points—if they had started at the mean location of the points, this would be equivalent to the mean deviation.

(E) Find the frequency of balls in each of the four quadrantsa rare frequency-based solution.

(F) Find the average distance between all pairs of points with a ruler—a good, long solution.

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Learning Experience

Activate learners’ prior knowledge

Central Tendency (e.g., average)
Range (e.g., max - min)

Schwartz, D. L., & Martin, T. (2004). Inventing to prepare for future learning: The hidden efficiency of encouraging original student production in statistics instruction. Cognition and instruction, 22(2), 129-184.

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Learning Experience

Create an awareness of knowledge gaps

Sample size
Outliers
Variability vs. central tendency vs. accuracy

Schwartz, D. L., & Martin, T. (2004). Inventing to prepare for future learning: The hidden efficiency of encouraging original student production in statistics instruction. Cognition and instruction, 22(2), 129-184.

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A Template for Your PS-I Assignment

What is your topic?
What are your learning goals?
What does a learner need to know to meet your learning goals?

Prior knowledge
Knowledge that needs to be learned

Describe your problem solving activity

How will your problem solving activity activate prior knowledge?
How will your activity create an awareness of knowledge gaps. That is, how it will create a need-to-know in the learner?

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Brainstorm your PS-I activity

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Learning Experience

Tips from the literature

"the problem is presented in the form of contrasting cases that differ in only one feature at a time" during the PS phase

a good design of PS-I works better in acquiring conceptual knowledge and the ability to transfer, rather than procedural knowledge

Loibl, K., Roll, I., & Rummel, N. (2017). Towards a Theory of When and How Problem Solving Followed by Instruction Supports Learning. Educational Psychology Review, 29(4), 693–715. https://doi.org/10.1007/s10648-016-9379-x