how to avoid common pitfalls in writing stem tests marcia kastner, ph.d. former mcas math assessment...

How to Avoid Common Pitfallsin Writing STEM Tests

Marcia Kastner, Ph.D.

Former MCAS Math Assessment LeadMassachusetts Department of Elementary and Secondary Education

Copyright © 2011 by Marcia Kastner

Outline

• Why are tests important?

• Definition of terms

• Examples of flaws in math questions

• How to fix the flawed questions

2Copyright © 2011 by Marcia Kastner

Why Are Tests Important?

• Used for accountability

• Provide information on what students know – and don’t know!

• For targeting instruction (from deconstructing test results)

3Copyright © 2011 by Marcia Kastner

Definition of Terms

• Valid test question: measures what it was designed to measure

• Pitfall: flaw in a test question that prevents it from being valid

• Parts of a multiple-choice question:– Options: answer choices– Key: correct option– Distractors: incorrect options

4Copyright © 2011 by Marcia Kastner

Math Testing Book

5Copyright © 2011 by Marcia Kastner

TESTING THE TEST

How to Recognize When Math Tests Are FlawedHow to Fix Them

Why We Should Care

(free books available after the presentation)

Presentation is based on pitfalls described in my book:

MarciaKastner.com

PITFALL:Right Answer for Wrong Reason (RAWR)

Example 1:

What is the median of the numbers below?

6, 2, 3, 1, 3

(Answer: 3)

( Not valid because:mean = 3; mode = 3; middle number in unordered list = 3)

(median = middle number in ordered list: 1, 2, 3, 3, 6)

6Copyright © 2011 by Marcia Kastner

How to Fix Example 1

Example 1 Revised:

What is the median of the numbers below?

7, 2, 6, 2, 3

(Answer: 3)

Change some of the numbers.

(mean = 4; mode = 2; middle number in unordered list = 6)

(ordered list: 2, 2, 3, 6, 7)

7Copyright © 2011 by Marcia Kastner

PITFALLS: Too Many Steps, Too Many Concepts, Option Sticks Out

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Example 2: (from New Eng. Common Assessment Program [NECAP], 2007)

Renata is a sales representative for a printer company. She sells two models of printers – Model P and Model Q.

• Last month she sold a total of 120 printers.• The ratio of Model P printers sold to Model Q printers sold was 3:5.

If Renata is paid a $25 commission for every Model P printer sold and a $20 commission for every Model Q printer sold, what was her total commission last month?

A. $1480B. $2475C. $2625 [key: 25(45) + 20(75)]D. $2760

(Not valid because:requires approx. 14 steps)

Pitfalls in Example 2

• Too many steps: approx. 14 steps

• Too many concepts:– Define variables– Model the bullet points as linear equations– Model the word problem as a system of linear equations– Solve the system of linear equations– Compute total commission

• One option sticks out: option A is different

Copyright © 2011 by Marcia Kastner 9

How to Fix Example 2

• Break up into multiple parts.

• Give partial credit for correct work shown.

Possible parts:

a) [write first bullet as equation]b) [write second bullet as equation]c) [determine amount of each model]d) [calculate total commission]

10Copyright © 2011 by Marcia Kastner

PITFALLS: RAWR, Not Testing Common Mistakes

Example 3: (from New York State Testing Program, 2010)

Simplify the expression below.

72 – 9 + 13

A. 37B. 39C. 41D. 43

(Answer: C)

11Copyright 2011 by Marcia Kastner

Pitfalls in Example 3

72 – 9 + 13

RAWR: 13 = 1 = 10 = 11 = 12 = etc.

Distractor logic:

A. 37 [49 – (9 + 3): PEMDAS and cube errors]

B. 39 [49 – (9 + 1): PEMDAS error]C. 41* [49 – 9 + 1: key]D. 43 [49 – 9 + 3: cube error]Common mistakes not tested by distractors:

1. square error: thinking 72 = 7 x 22. perform operations left-to-right

12Copyright 2011 by Marcia Kastner

How to Fix Example 3

Example 3 Revised:

What is the value of the expression below?

72 – 9 + 23

A. 11 [14 – 9 + 6: exponent errors]B. 21 [(14 – 9 + 2) x 3: PEMDAS & exponent

errors]C. 32 [49 – (9 + 8): PEMDAS error]D. 48 [49 – 9 + 8: key]

(Answer: D)

Change the expression and distractors.

(testing common mistakes)

13Copyright 2011 by Marcia Kastner

PITFALL: Implausible Distractors

Example 4 (same as Example 1 Revised but as a multiple-choice question):

What is the median of the numbers below?

7, 2, 6, 2, 3

A. 3B. 6C. 9D. 12

(Answer: A)(Not valid because:cannot determine how errors made)

14Copyright © 2011 by Marcia Kastner

How to Fix Example 4

Example 4 Revised:

What is the median of the numbers below?

7, 2, 6, 2, 3

A. 2 [mode]B. 3 [key: median]C. 4 [mean]D. 6 [middle number of unordered list]

(Answer: B)

Change the distractors.

(can determine how errors made)15Copyright © 2011 by Marcia Kastner

Your Chance to TEST THE TEST

Find the pitfalls in the following examples.

16Copyright © 2011 by Marcia Kastner

What Is the Pitfall in Example 5?

Calculators Allowed: All types

Example 5 (same as Example 1 Revised except that a calculator is allowed):

What is the median of the numbers below?

7, 2, 6, 2, 3

(Answer: 3)

(Pitfall: Calculator, not student, solves the question.Not valid because: graphing calculators determine median.)

17Copyright © 2011 by Marcia Kastner

How to Fix Example 5

Calculators Allowed: All types except graphing calculators, OR no calculators allowed

Do not allow graphing calculators.

18Copyright © 2011 by Marcia Kastner

What Are the Pitfalls in Example 6?

Example 6: (from New England Common Assessment Program [NECAP], 2010)

Courtney walks three laps around a ¼-mile track. How many feet does she walk? [1 mi. = 5280 ft.]

A. 440 ft. [1/3 x ¼ x 5280]B. 1320 ft. [¼ x 5280]C. 3960 ft. [key: 3/4 x 5280]D. 7040 ft. [4/3 x 5280]

(Answer: C)

19Copyright © 2011 by Marcia Kastner

Pitfalls in Example 6

• Confusing & imprecise language: “laps around a ¼-mile track”

(Particularly disadvantages ELL and SPED students)

• Biased context: track

• Too many concepts– Fractions– Unit conversion

20Copyright © 2011 by Marcia Kastner

How to Fix Example 6

• Break up into multiple parts & allow partial credit.

• Add diagram showing oval track.

• Show how distance around is ¼ mile.

• Eliminate or explain word “lap.”

• Bold the word “three” or replace it with “3.”

21Copyright © 2011 by Marcia Kastner

Summary

• Tests must be valid– Scrutinize test questions for pitfalls

– Revise questions to remove pitfalls

• Diagnose students’ incorrect answers to see where they went wrong

• Focus instruction on areas that need improvement

22Copyright © 2011 by Marcia Kastner