Running head: Growth Mindset Assessments1
Using Assessments to Promote Growth Mindset in College Algebra
Hannah M. Lewis, Kady Schneiter, and David Lane Tait
Mathematics and Statistics, Utah State University, Logan, Utah
Growth Mindset Assessments2
Using Assessments to Promote Growth Mindset in College Algebra
Abstract
Scientific evidence highlights the positive impact of a growth mindset on student
achievement. Students with a growth mindset view errors and obstacles as opportunities for
growth and welcome challenges and the opportunity to learn from their mistakes. Much has been
written about promoting growth mindset through lectures and attitudes, however, assessments
can also be an important avenue for encouraging a growth mindset in students. In this paper, we
describe how we used assessments to promote growth mindset in a college algebra class. In the
sections that follow, we discuss the need for these assessments and the principles that underly
their development. We then describe the three-part structure of the assessments we created, how
they were implemented, how feedback and scoring was addressed, and student response to them.
This is a novel approach to assessment that promotes growth mindset and lowered anxiety levels
as was shown in the student survey responses. This reframed how we looked at summative
assessments and allowed us to introduce formative assessment elements, like reworks and group
feedback, into many aspects of the summative assessments. Later research will be used to show
more definitive results for the change in mindset of students.
Keywords: assessment, growth mindset, formative, summative
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Using Assessments to Promote Growth Mindset in College Algebra
Introduction to Assessments
Formative and summative assessments are the most important learning experience that
we facilitate for students, as teachers, to measure our student progress and achievement on
learning objectives. These assessments also perform the important role of helping students
understand their progress and achievement of those objectives. Assessments do not just attempt
to evaluate what knowledge and skills students have learned; they can also be used to motivate
them to learn from their mistakes. Students can ignore instructor feedback and classroom
interactions. However, if they want to move forward with their education, they must participate
in the assessments teachers have designed to determine their achievement of learning objectives.
Using assessments designed to promote growth mindset can not only encourage students to pay
attention to feedback, but it can also create an environment where students want to learn and
grow from their own and other classmate’s mistakes.
Traditional mathematics exams (multiple choice, free response, matching, and/or short
answer), in which a student responds to prompts and is given a score in return does not
necessarily fit a growth mindset framework. These single attempt exams may not promote
opportunities for students to learn from their mistakes. When a student guesses a correct answer
while not achieving the expected learning objective, they are not being provided with the
opportunity for growth or reflection because they are assumed (in error) of achievement of the
learning objective. Changing from the traditional methods of assessments to assessments that
assess for learning with a growth mindset framework has potential to greatly improve students’
experiences and learning. Instructors can adapt assessments to promote growth mindset in the
following ways:
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● Remove initial scoring from the assessments.
● Provide diagnostic and encouraging feedback on all assessments.
● Provide structured opportunities for students to show achievement of the
objectives that were incorrect on the first assessment attempt.
● Provide a rubric that informs students of their current achievement of the learning
objectives.
● Use multiple forms of assessment that include some, or all, of the following:
group work, papers, long and short answer free responses, and presentations.
● Fit the assessment questions to the learning level that the learning objective was
taught at.
● Final scoring is assigned to match the weight of the corresponding weighted
objective instead of the difficulty level of the problem.
It is anticipated that when these changes are implemented in a university setting,
instructors will likely see an increase in student performance and in their attitudes and mindset
about mathematics. We used a different structure of assessments to promote growth mindset in a
college algebra class. The need for these assessments is analyzed and the principles that underly
their development are discussed. This is followed by a description of the growth mindset
structured assessments we created, how they were implemented, and the student survey
responses.
Motivation for a Growth Mindset Assessment Structure
The way that teachers assess students plays an important role in the mindsets students
develop. A mindset is a self-perception that people hold. According to Dweck (2007, p. 68-69),
those who have a fixed mindset believe traits like intelligence are fixed and as a result they spend
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time documenting their intelligence instead of trying to learn and grow through effort.
Alternatively, those with a growth mindset believe that intelligence and talents can be developed
through hard work and dedication. Having a growth mindset has been shown to have a positive
impact on student achievement (Dweck, 2007, p. 70).
Dweck’s (2016) research on growth and fixed mindsets suggests that students who have
adopted a fixed mindset shy away from challenges because poor performance might either
confirm they cannot learn or indicate that they are less intelligent than they think. When students
with fixed mindsets fail at something, like an assessment, their tendency is to tell themselves
they cannot or will not be able to do it, or they make excuses to rationalize the failure.
In a growth mindset people believe that intelligence, talents, and math skills can be
developed through hard work and dedication (Dweck, 2016). Students who embrace a growth
mindset may learn more, learn it more quickly, and view failures and challenges as opportunities
to increase their learning and growth. As a result, mindset can be a positive predictor of
achievement at all academic levels.
The correlation between mindset (or attitude) and achievement has been shown in
university students by Maure and Marimon (2014). They looked at the attitudes and achievement
of 1076 college students from Panama and Mexico. Their results showed academic achievement
correlates positively with attitude with a correlation coefficient of r = .725 (Mexico) and r = .829
(Panama) and p < .01. They stated that, “The result suggests that the greater the attitude towards
mathematics the greater is the students’ academic achievement (Maure & Marimon, 2014, p.
767).”
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At Utah State University, Bagley (2015) found that mindset was a good predictor of
student outcomes in developmental math courses, especially in college pre-algebra (Math 1010)
in which students with a growth mindset performed much higher than students with a fixed
mindset. He found that mindset had a statistically significant effect on students’ pass rate in
college pre-algebra. Bagley stated, “the odds of passing for a student with a Growth mindset
were 3.00 times the odds for a student with a Fixed mindset (pg. 28)”. This was confirmed in
overall percentage of points earned as well as scores on exams and pass rates in math courses at
the developmental (900) and freshman (1000) level.
Teacher’s choice in method of assessing student achievement has an important role in the
mindsets that these students develop. In fact, providing constructive formative feedback as a
method of evaluating the assessment encourages students to have a growth mindset (Yeager et
al., 2013). Boaler and Confer proposed a method of assessment she called ‘Assessment for
Learning’ for evaluating assessments that can change the relationship students have with their
learning from anxiety to growth. This method uses diagnostic comments instead of traditional
grading, as well as self and peer evaluations to bridge the gap between what students need to
know and their current understanding. These strategies encourage mathematical problem solving,
creativity, and persistence. Currently most assessments do not focus on this. Instead, they test
what is easy to assess, alculations with a single correct answer (Boaler & Confer, n.d).
Participants, Settings, and Materials
For this work, we developed and used assessments designed to foster growth mindset.
These assessments were used in three summer semester college algebra/pre-calculus courses.
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Two of these classes met for seven weeks and one was a fourteen-week session spanning the
entirety of the two seven-week sessions. Of the 50 students in the classes, 23 responded to a
survey on their experience that was administered through Qualtrics and consented for us to use
their responses. The study was approved through IRB at Utah State University with the protocol
#9331.
The participants ranged in age from 18-40, with the majority of students between the ages
of 20-30. The majority of the students were white. About half were male and half female. These
demographics are consistent with the university undergraduate population demographics.
Assessment Design Principles
We created the assessments based on weighted learning objectives with corresponding
learning levels that provided the structure of the lesson plans for the course. The type of prompt
given was determined by the learning level associated with the learning objective (Cangelosi,
2002).
In the following table is given the learning levels with the typical instructional strategies
that are used as given by Kohler et al. (2010, p. 37). The assessment type was chosen to mirror
the learning level and instructional strategy. To determine the assessment portion assigned,
student time and the need for communication was analyzed.
LEARNING LEVEL
INSTRUCTIONAL
STRATEGIES
ASSESSMENT
TYPE
ASSESSMENT
PORTION
Construct a Concept
Inquiry Instruction
Formative in Class
Formative
Discover a Relationship
Multiple Part
Group Portion
Simple Knowledge
Direct Instruction
Short Answer
Proctored Portion
Algorithmic Skill
Show Work (Math)
Proctored Portion
Comprehension and
Communication
Direct and Inquiry
Instruction
Long Answer
(Sentence)
Essay/Group Portion
Application
Multi Part
Group Portion
Creative Thinking
Inquiry Instruction
Long Answer
Essay Portion
Willingness to Try
Varies
Varies
Appreciation
Varies
Varies
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Table 1
Some readers might see some similarities between Learning Levels and Bloom’s taxonomy. The
advantages of using the learning levels by Cangelosi instead are they are specifically designed
toward mathematics and no single level is considered more important than another.
The Assessments
Students enrolled in college algebra participated in three-unit assessments over the course
of the semester. Each assessment consisted of three parts: (a) a short answer portion that was
proctored in the university testing center, (b) a take home essay portion, and (c) a project that
was completed in groups. The assessments were scored in terms of student achievement of
weighted objectives. Students did not see numerical scores. Instead, they were only informed of
their achievement through structured constructive feedback. Students were able to rework missed
testing center assessment problems (part a) and complete additional similar problems as part of
the assessment process. The students were encouraged to have classmates read and give
feedback on their essays (part b) before their final submission. The nature of group work
facilitated feedback on the group test portion (part c) before final submission. The design of
these assessments allowed students multiple attempts to show achievement of objectives at the
stated learning level, allowed students to learn from their mistakes, and scaffolded productive
struggle.
Scores on the assessments were converted to numerical representations that the students
did not have access to. They were able to see their progress in the course through achievement of
weighted objectives. Students saw their level of achievement on each exam prompt with three
categories: Exceeds Expectations, Meets Expectations, and Needs Work. They also received
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personalized constructive feedback. Students received letter grades for each assessment after all
components, including any reworks, were complete.
Short Answer Proctored Assessment Segment
For the short answer segment of each assessment, participants gave short, written
responses to a series of prompts targeting the relevant objects. See Examples 1A and 1B below.
The short answer segments had 16, 14, and 16 prompts respectively.
•
Objective: Students will algebraically manipulate complex numbers. (Algorithmic Skill 3%)
• Prompt: Write the following in the standard form +
3
(
2 − 5
)
−
(
1 + 4
)
Example 1A: An objective and prompt from the short answer portion of an assessment.
•
Objective: Students will learn the basic facts about the complex zeros of polynomials. (Simple
Knowledge 3%)
• Prompt: Find the remaining zeros of the polynomial P(x) with real coefficients that has a
degree of 6 and the zeros 2i, 4+i, -1+i.
Example 1B: An objective and prompt from the short answer portion of an assessment.
In the feedback for each item, students were given instructions for correcting the original
mistakes and an additional prompt to respond to learn from their mistakes and show their
achievement of the objective (See Examples 2A and 2B). Correcting the mistakes and responding
to the additional prompt was optional but facilitated deeper learning. Students had two weeks to
complete corrections after they received the assessment feedback. After completing the rework
prompt on their own, they met with the instructor or a recitation leader to ensure they had
achieved understanding of the objective at the appropriate learning level.
● Rework:
• Rework the original problem describing your mistake
• Put the following in standard form:
3+2
2+5
Why did you multiply by (2 − 5)? Why did you also multiply it on top?
Example 2A: Rework prompt.
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● Rework:
• Rework the original problem describing your mistake
• Create a 5th degree polynomial with real coefficients that has 1 real zero and 4
imaginary zeros.
Example 2B: Rework prompt.
Each of the unit exams had one rubric for the initial exam-scoring with specific detailed
feedback for each item (see Examples 3A and 3B), and a second for the rework opportunity (see
Examples 4A and 4B).
● Rubric for original prompt:
• +4 for using correct algebra to find the correct answer in the correct form.
• +3 for minor algebraic mistakes and the answer is in the correct form.
• +2 for using correct algebraic tools, but final answer is in the wrong form.
Example 3A: Rubric for original prompt.
● Rubric for original prompt:
• +1 for each zero found correctly as the conjugates of the given zeros.
Example 3B: Rubric for original prompt.
● Rubric for rework prompt:
• All points back if problem is now correct and answers to additional prompts are
satisfactory.
• ½ points back for minor errors and showing increase in understanding.
Example 4A: Rubric for rework prompt.
● Rubric for rework prompt:
• All points back for using a real zero and using complex conjugates for the other
pairs of complex zero.
Example 4B: Rubric for original prompt.
Essay Exam Segment
The second component of each exam was an essay. Students used this portion to respond
to three to five prompts (See Example 5) in two to five pages total. This portion was open notes
and completed outside of class. The instructor gave individual feedback in the Instructor
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Comments section for each student's submission on Canvas. Students were then able to rewrite
the portions of the paper that did not show achievement of the objective.
Objective: Apply exponential functions to real world problems. (Application 6%)
Prompt: Tell me about a large dream purchase of yours (more than $5000). Say you have
$5000 to invest at an annual interest rate of 11%. When would you have enough to purchase
your item if the interest is compounded:
• Yearly?
• Quarterly?
• Monthly?
• Daily?
• Continuously?
Show ALL of your by hand calculations.
Example 5: A prompt for the essay portion of an exam.
Rubric:
+3 using the correct formulas
+2 for describing a dream purchase
+1 showing work
Example 6: Rubric for example 5 from the essay portion of an exam.
Group Project Exam Segment
The third part of each exam was a groupwork segment consisting of three to five prompts
(see Example 7) that students responded to in groups of three to five. The students were given
some class time to work on this portion but also worked outside of class. These questions were
mostly application questions. Group members gave each other feedback for this portion of the
exam. This structure allowed the students to rework their answers before the final draft was
turned in. The rubric for the group project is shown in Example 8.
Although they had the help of their group, each member turned in a full-completed
project in their own words and the projects were graded individually.
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1. Objective: Students will comprehend and communicate the important properties of
functions. (Comprehension and Communication 3%)
o Give two reasons you know this is a function.
o Write the piecewise function rule for the graph.
o What is the domain? Justify your answer with at least one
sentence.
o What is the range? Justify your answer with at least one
sentence.
o Give one other observation about this graph.
Example 7: A prompt from the group project portion of the exam.
Rubric:
+1 for including vertical line test in reasons.
+1 for the piecewise rule written correctly
+1 for correct domain and range
Example 8: Rubric for example 7 from the group portion of an exam.
Student Responses
Student response was positive overall. Of the 33 enrolled students that agreed to have
their data used for the analysis, 23 also agreed to complete an anonymous survey within 20 days
of the end of the course. In that survey, many student comments showed a mindset shift from a
fixed mindset toward growth mindset. When students were asked to compare their feeling about
math before the class compared to after the class, the responses were coded as representative of a
fixed, neutral, or growth mindset. These were coded based on phrases typically used in each
mindset. For example: “not a failure” or “learned from mistakes” were coded as growth, while “I
can’t learn” is coded as fixed. Of the 23 responses to the feeling about math before participating
in the course, 8 were coded as fixed, 11 as neutral, and 4 as growth. Their responses about their
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feelings toward math after participating in the course had 0 coded as fixed, 6 as neutral, and 17
as growth mindset.
The students indicated that they felt that these assessments were more representative of
their true knowledge of the material than traditional math exams. Of the 23 responses to a
question on their feelings about the test structure for this course, 8 responded that they felt the
assessments helped them to learn the material, lower their anxiety, and show their true
understanding of the material more effectively.
Some examples of student comments follow:
“I felt like in this class it was ok to fail or answer wrong and instead of being
shamed for not getting the answer right I learned from my mistakes.”
“I loved the focus on concepts instead of numbered points- I worked harder but
was also more relaxed knowing a small mistake in arithmetic wouldn’t ruin the grade."
“The feedback was priceless."
“I loved it! It helped me go back and relearn concepts that didn’t stick at first
which makes me more confident going into my next class because I know I didn’t miss
anything.''
“I learned to take my time when doing math problems and not race through it. I
learned that it's ok to not remember everything, ... I'm not a failure and that there is
always room for improvement!''
“Math has always been difficult, and I have taken this course before, I now know
that I just need more patience and practice and I can do math really well.''
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Although the comments were overwhelmingly positive, there were a few negative
comments coming from 2 of the 23 students that responded to the survey. For example:
“I didn't like writing papers. I prefer solving equations.”
“I can write. Writing is not the issue. My issue is that papers in math classes are wrong.”
Discussion
The implementation of this process allowed me and the other instructor to help students
form a better relationship with math than they would have been able to otherwise. We saw an
increase in growth mindset and a decrease in math anxiety by watching and interacting with the
students. When we designed the study, we expected this to occur and were pleased to see this
happening even before receiving the student survey responses. The opportunity to rework missed
prompts was very important in the process of helping student understanding of mathematical
content. However, meeting with every student that wanted to participate in the rework
opportunities was very time consuming. There is, however, a trade off with the time invested and
properly determining student understanding.
Writing papers allowed some students to have a creative outlet in math class as well as
demonstrate that they can communicate about the mathematics. Based on student comments,
students that struggled with math anxiety, dyslexia or other disabilities found the papers allowed
them to clarify what they already understood and what they needed to go back and work on
more. It may be possible to obtain this benefit by administering the essay questions in proctored
setting and making them available to students before the assessment.
Group work was the most well liked and helpful aspect of the exam structure for the
students based on the survey comments. Working with other classmates allowed them to get
feedback from sources other than the instructor. It also allowed the students the opportunity to try
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and explain the mathematical concepts and processes to other students in a lower anxiety setting.
This process increased understanding as well as highlighted gaps in understanding allowing them
to be filled.
Conclusion
In conclusion, we have showed that removing initial scoring from the assessments while
providing actionable and positive feedback on the rubrics of all formative assessments increased
the growth mindset responses. The original intent of this study was to pilot a larger project. The
development of the assessments as a useful tool to hopefully increase the growth mindset in
students was the goal. Since the results are so encouraging, later research will be used to show
qualitative and quantitative results for the change in growth mindset and anxiety level of
students. Providing structured opportunities for students to show achievement of the objectives
that were incorrect on the first assessment attempt reduced, in multiple ways, many students’
math and test anxiety levels and resulted in growth mindset coded responses on the survey.
The multiple forms of assessment had a mixed result in the student responses. Students
had the most positive responses to the group work and the most negative responses (although
still few) were toward the paper portion. These results, as well as the instructor notes on
usability, will guide the future improved structure of these assessments.
It was very exciting to see a large majority of student responses show an increase in
growth mindset responses in their reflection on the assessment experience. The large number of
responses indicating lower anxiety as a result of this assessment structure was also very
promising. Although we were limited by the small number of students that were registered for
the course in the summer semester, further research into the impact of growth mindset structured
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assessments will be done to show the impact on achievement as well as mindset and anxiety
levels.
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