DePaul Assessment Certificate
Culminating Project
Assessment of STEM Center
Algebra Initiative Learning Outcome
Max Barry
Department Assistant
STEM Center
1
Brief Overview of the
Algebra Initiative
2
Algebra Initiative Goals
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.
3
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
4
 Instructors:
 Dr. David Jabon, Director of the Quantitative Reasoning Center and Associate
Professor of Mathematics/STEM Studies
 Dr. Lynn Narasimhan, Director of the STEM Center and Professor of
Mathematics
 Course Sequence
 Three 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.
5
Assessment Design
6
Learning Outcome Studied
Students will understand the logic underlying the processes of
algebra, such as the process of finding solutions to equations and
inequalities.
7
Equations and
Identities
Assessment Tool
8
Assessment Tool
Asks 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+20
Incorrect: 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; 2x1=2x+3; |x+2|=-4; 2x+5=2x+6; 2x+3=2x+7
Incorrect: 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
9
Assessment Tool
Asks students to:
• 2 (5 parts): Determine how many
answers a given equation has.
12/12
12*/12, x=20
12/12
8/12
12/12
*Correct/Incorrect Answers taken from Pre-test
10
Assessment Tool
Asks 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.
11
Assessment Tool
Asks students to:
• 3. Part 2: In your own words, explain
what is meant by an identity.
12
• 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?
• 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.
• 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.
13
5-Point Analytic Rubric for question 3, part b:
Question 3b
In your own
words,
explain what
is meant by
an identity.
5
Student
correctly
defines an
identity with a
complete
explanation
using clear
language.
4
3
2
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.
1
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.
14
3b. Rubric Pretest Results
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.
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.
15
Results:
Pre-Test/Post-Test
16
Paired T-Test
 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.
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.
17
3b. Rubric Pre- and Post-Test Results Grouped by Post-Test Score
5: Student correctly defines an identity with a complete explanation using clear language.
8623 A statement that will always be true.
4
8623 An equation that has infinite solutions (or all real numbers) - both sides are equivalent.
5
This means that one side equals the other; both sides are equivalent expressions and will have the same output no matter what
2269 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
4: Student correctly defines an identity and includes a short explanation which requires
elaboration.
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
3: Student’s definition of an identity is basically correct, but the explanation is somewhat confusing.
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 equaldefines
to itself.
1:
an identity.
2: Student
Student incorrectly
gives an example equation,
but does not make further effort to define an
2866 The value on both sides is the same.
identity,
or the
definition
hasby aaddition
significant
flaw.
8337 The starting
amount
is not changed
or multiplication.
2866 Both sides of equation have same value.
2003 An
When
there are
infinitely many
8337
operation
or procedure
that solutions.
doesn't change the
4961
When
the
equation
is
true
real numbers.
2003 An identity is a way of saying for
thatallthere
are infinitely many solutions.
4961 It means that the expression on both sides of the equation are the same
3
4
1
1 2
2
3
5
3
18
Paired T-Test Results
Student
Identifier
573
1478
1797
2003
2269
2866
4384
4961
5727
8337
8623
Average
Pre
11.2
6.4
10.6
9.8
12
7.6
10.6
11
9.2
9.4
10.6
9.9
Post
Difference
11.2
0
10.2
3.8
11.6
1
10.8
1
12
0
9.2
1.6
11.6
1
8.2
-2.8
9.2
0
9.4
0
12
1.4
10.5
0.64
P-Value: .11
19
Histogram of Post Minus Pre Test
6
5
4
3
2
1
0
-3
-2
One student did very well on the pre-test,
and relatively poorly on the post-test.
-1
0
1
Scored higher on
post test.
2
3
One student improved h/er
score significantly.
20
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.
21
Item Analysis
1.200
1.000
0.800
Pretest
0.600
Postest
0.400
0.200
0.000
1a
1b
1c
82%
1d
92%
2a
2b
2c
2d
82%
2e
3a
73%
22
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