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DePaul Assessment Certificate Culminating Project

Assessment of STEM Center Algebra Initiative Learning Outcome

Max Barry Department Assistant STEM Center

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Brief Overview of the Algebra

Initiative

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The Algebra Initiative program was created in 2003 to raise the standard of mathematics instruction to the national level.

Its goal, as stated on the Chicago Math and Science Initiative website, is “to provide a series of courses that will prepare elementary teachers to deliver a high-quality algebra course to any well-prepared middle grade student in their school.”

“In 2003 eighth-grade students nationwide took algebra at a rate of 33%… In the city of Chicago, the comparable rate was a mere 7%.”

Jabon, D., Narasimhan, L., Boller, J., Sally, P., Baldwin, J. & Slaughter, R. (2010). The Chicago Algebra Initiative. Doceamus, 57(7), 864-866.

Algebra Initiative Goals

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Algebra Initiative Program Stats Since 2003-2004 Academic Year

Over 250 Chicago Public School teachers have enrolled in the STEM Center’s Algebra Initiative courses.

Citywide, 597 teachers have been certified to teach algebra in K-8 schools.

597

250

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Course SequenceThree Courses all numbered STEM 698:

Winter—Topics for Mathematics and Science Teachers-Algebra/Middle School/Teach/I

Instructor—Dr. Narasimhan.Spring—Topics for Mathematics and Science Teachers-Algebra/Middle

School/Teach/II Instructor—Dr. Jabon

Fall—Topics for Mathematics and Science Teachers-Algebra/Middle School/Teach/III

Instructor—Dr. Narasimhan

Administered assessment half-way through 2014-15 courses I and II.

Instructors:Dr. David Jabon, Director of the Quantitative Reasoning Center and Associate

Professor of Mathematics/STEM StudiesDr. Lynn Narasimhan, Director of the STEM Center and Professor of

Mathematics

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Assessment Design

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Learning Outcome StudiedStudents will understand the logic underlying the processes of

algebra, such as the process of finding solutions to equations and inequalities.

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Equations and Identities

Assessment Tool

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Assessment ToolAsks students to:

• 1 a-d: provide examples of equations with specified sets of answers.

(a) One Solution:Correct : 3x+2=5; 5x = 10; x+5=7; n+3=5; 5x=30; 4x=8; x+2=4; x+1=8; 3x+5=12; x+2=4; 2x+5=11; 2x+3=7 (b) Two Solutions:Correct: |3x+2|=5; x^2=25;|x+2|=5;|n+3|=5;|x|=40;|x|=2; x^2=64;|x|=7; x^2+3x-4=0; x^2+9x+20 Incorrect: |5|=+-5 ; x=√64

(c) An infinite number of solutions:Correct: 10x=10x; x+5=x+5; 6x+18=6(x+3); x+2=x+2; 2x+4=(8x+16)/4; 2x=2x; y=3x+5; 3(x+5)+5=3x+20Incorrect: Blank; 4-3x=5x+7-2x; 3x + 2 > 5; x>2

(d) No solutions:Correct: x+12 = x-3; 3x+10=3x-10; x+5=x+4; x+2=x-2; 2x-1=2x+3; |x+2|=-4; 2x+5=2x+6; 2x+3=2x+7Incorrect: Blank; 3x+14=6x+27; x+1=4, x=2; x^2+3x+1=y or 2x+1=2x

*Correct/Incorrect Answers taken from Pre-test

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Assessment Tool

Asks students to:

• 2 (5 parts): Determine how many answers a given equation has.

8/12

12/12

12*/12, x=20

12/12

12/12

*Correct/Incorrect Answers taken from Pre-test

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Assessment ToolAsks students to:

• 3. Part 1: Which of the equations in question 2 are also identities?

2(x+6)=2x+12

8/12 students answered correctly on pre-test.

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Assessment ToolAsks students to:

• 3. Part 2: In your own words, explain what is meant by an identity.

• What is an Identity?• An equation which, when one plugs in any real number for the

variable, the left side is the same as the right side.

• Why are identities a good tool to assess a student’s/teacher’s understanding of the underlying logic of an equation?

• Through the process, one creates a series of equivalent equations, each of which is generally simpler.

• Typically, one can read off the solution set from the last equivalent equation in the series. This concept can be favorably compared to mere procedural understanding.

• The two sides of an identity look different, but through manipulation of their structure, to use a word from the Common Core, they can be progressively simplified to reveal an equality.

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5-Point Analytic Rubric for question 3, part b:Question 3b 5 4 3 2 1

In your own words, explain what is meant by an identity.

Student correctly defines an identity with a complete explanation using clear language.

Student correctly defines an identity and includes a short explanation which requires elaboration.

Student’s definition of an identity is basically correct, but the explanation is somewhat confusing.

Student gives an example equation, but does not make further effort to define an identity, or the definition has a significant flaw.

Student incorrectly defines an identity.

Sample of a “5”: An equation which, when one plugs in any real number for the variable, the left side is the same as the right side.

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3b. Rubric Pretest Results

4: Student correctly defines an identity and includes a short explanation which requires elaboration.• That they represent the same values on both sides of the equation• A statement that will always be true.• The value on both sides is the same.• Both parts of the equation are equivalent

3: Student’s definition of an identity is basically correct, but the explanation is somewhat confusing.• They are equivalent.• Identity is a rule or legal move that makes a number equal to itself. It is true for all values.

2: Student gives an example equation, but does not make further effort to define an identity, or the definition has a significant flaw.• When there are infinitely many solutions.

1: Student incorrectly defines an identity.• The starting amount is not changed by addition or multiplication.• a+-a=ø• Whenever you multiply a number by 1 your answer will be 1.

5: Student correctly defines an identity with a complete explanation using clear language.• When the equation is true for all real numbers.• This means that one side equals the other; both sides are equivalent expressions and will have

the same output no matter what the input.

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Results: Pre-Test/Post-Test

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Paired T-Test

Notes: • 12 was the highest possible total score.

• Each part of Question 1 and 2, and part “a” of Question 3 were worth 1 point.

• 3b was weighted, and a correct answer was rewarded 2 points.

12 Pre-Test Students; 13 Post-Test Students; 11 Pre- and Post-tests compared. 1 student who took the pre-test was absent for the post-test.

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3b. Rubric Pre- and Post-Test Results Grouped by Post-Test Score

4: Student correctly defines an identity and includes a short explanation which requires elaboration.

3: Student’s definition of an identity is basically correct, but the explanation is somewhat confusing.

2: Student gives an example equation, but does not make further effort to define an identity, or the definition has a significant flaw.

1: Student incorrectly defines an identity.

5: Student correctly defines an identity with a complete explanation using clear language.8623 A statement that will always be true. 48623 An equation that has infinite solutions (or all real numbers) - both sides are equivalent. 5

2269This means that one side equals the other; both sides are equivalent expressions and will have the same output no matter what the input. 5

2269 That one side of the equation is equivalent to the other; for any input you will get the same output. 5

1797 Both parts of the equation are equivalent 4

1797 That both parts of the equations are equivalent. 4

4384 That they represent the same values on both sides of the equation 4

4384 When the value of x can be all real numbers. 4

1478 a+-a=ø 1

1478 2x+12=2x+12; When something is equal to itself. 3

5727 Identity is a rule or legal move that makes a number equal to itself. It is true for all values. 3

5727 When the value is equal to itself. 3

2866 The value on both sides is the same. 4

2866 Both sides of equation have same value. 3

4961 When the equation is true for all real numbers. 5

4961 It means that the expression on both sides of the equation are the same 3

2003 When there are infinitely many solutions. 2

2003 An identity is a way of saying that there are infinitely many solutions. 2

8337 The starting amount is not changed by addition or multiplication. 1

8337 An operation or procedure that doesn't change the 1

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Paired T-Test ResultsStudent

Identifier Pre Post Difference573 11.2 11.2 0

1478 6.4 10.2 3.81797 10.6 11.6 12003 9.8 10.8 12269 12 12 02866 7.6 9.2 1.64384 10.6 11.6 14961 11 8.2 -2.85727 9.2 9.2 08337 9.4 9.4 08623 10.6 12 1.4

Average 9.9 10.5 0.64 P-Value: .11

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-3 -2 -1 0 1 2 30

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3

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5

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Histogram of Post Minus Pre Test

Scored higher on post test.

One student did very well on the pre-test, and relatively poorly on the post-test. One student improved h/er

score significantly.

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Conclusions

• The students’ scores improved, but the improvement was not statistically significant given P-Value .11.

• The high scores suggests that the learning outcome—students will understand the logic underlying the processes of algebra, such as the process of finding solutions to equations and inequalities—has been successfully achieved.

• The students scored well on the pre-test, so there was likely some ceiling effect on the post-test scores.

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1a 1b 1c 1d 2a 2b 2c 2d 2e 3a0.000

0.200

0.400

0.600

0.800

1.000

1.200

Item Analysis

PretestPostest

82% 82% 73%92%

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