JOURNAL CRITIQUE: MATH AND THE DIFFERENTIATED CLASSROOM 2
Journal Critique: Math and the Differentiated Classroom
In the article Differentiated instruction enhances sixth-grade students' mathematics
selfefficacy, learning motives, and problem-solving skills (2020), educational researchers Lai,
Zhang, and Chang examine the effectiveness of differentiation in the 6th grade math classroom.
The researchers sought to prove that differentiated instruction intervention was essential in
promoting 6th grade students’ mathematics self-efficacy (MSE), mathematics learning motives
(MLM), and mathematical problem-solving skills (MPSS). These three measurements being
indicative of a student’s success in mathematics learning. The researchers employed a
longitudinal approach with a pretest and posttest design with 25 students, and used 3 instruments
for quantitative data collection. Lai, Zhang, and Chang (2020) conducted a year long study of
students receiving differentiated instruction in the hopes of proving that there would be great
improvement in the post test results of students’ MSE, MLM, and MPSS.
Summary
The article Differentiated instruction enhances sixth-grade students' mathematics
selfefficacy, learning motives, and problem-solving skills (Lai, Zhang & Chang, 2020)
conducted a year long experiment with twenty-five 6th grade math students in a differentiated
classroom. The researchers created a longitudinal study designed with a pre-test and post-test to
check for student success across three instruments for quantitative data collection. The
researchers used 6th grade students following a study by Urdan and Midgley (2003) that showed
empirically in a sample of American students that student self-efficacy begins to decline in 7th
grade or earlier, specifically in mathematics.
Lai, Zhang, and Chang conducted measures on three specific areas of mathematics
learning, mathematics self-efficacy (MSE), mathematics learning motives (MLM), and
JOURNAL CRITIQUE: MATH AND THE DIFFERENTIATED CLASSROOM 3
mathematical problem-solving skills (MPSS). These areas were identified as the most indicative
of success in mathematical learning. The pre-test and post-tests (beginning of the year of
instruction and end of the year) scores for the whole scale and for the Self-Efficacy for
Mathematical Learning sub-scales were significantly higher. This supported the researchers’
original hypothesis that there would be significant growth in the students’ mathematics self-
efficacy scores after only one year of differentiated instruction.
Analysis
The research presented in this article was quantitative with measures success in the test
group of twenty-five 6th Grade students. The participants comprised of an elementary class in a
southern Taiwanese elementary school. The elementary teacher and her colleagues voluntarily
attended professional development trainings and professional developments in order to prepare
for the year-long experiment. The head teacher for the class in question, then worked with her
colleagues to develop two major lessons that would teach the content needed for the pre and
post-tests, using the differentiation methods agreed upon by the mathematics teacher learning
community formed through professional development (Lai, Zhang & Chang, 2020).
The content used for the pre and post-tests were lessons on algebraic fractions and related
concepts. Students took the pre-test before receiving any new instruction regarding the topic,
then received in-depth and differentiated instruction across two multi-day lessons. The
administered testing used the twenty-three metrics in the, “Mathematics Self-Efficacy
Instrument, which was developed and validated by Chang, with two sub-scales, to assess the
participants' MSE” (Lai, Zhang & Chang, 2020).
The research and testing presented in the article are exceedingly thorough with metrics
that cover four major dimensions of learning; academic achievement, meeting the expectations
JOURNAL CRITIQUE: MATH AND THE DIFFERENTIATED CLASSROOM 4
of others, self-regulated learning, and enlisting social resources and parental support. All
indicators of future academic success according to the researchers. The scale of the testing,
however, was limited and in my opinion too restricted to yield accurate results. While one class
tested in one major standard in one content area showed improvement, in order to fully confirm
the researchers’ hypothesis, multiple sample classes and a control class should have been used.
Personal Application
Differentiation is an essential part of a teacher’s repertoire. As Tomlinson states,
“differentiation calls on a teacher to realize that classrooms must be places where teachers purse
understandings of compelling teaching and learning every day,” (Tomlinson, 2017). As a math
teacher, differentiation is an essential method to help students reach mastery of math concepts
and practice. Meeting the needs of our diverse learners in the classroom and creating a warm,
welcoming, and nurturing a classroom environment is a reflection of our duty towards Christ.
Phillipians 2:4 tells us, “not looking to your own interests but each of you to the interests of the
others” (King James Bible, 2023). By differentiating, we are looking after the needs and
academic well-being of our students.
Conclusion
The modern classroom is full of learners with a swath of diverse needs and interests.
Differentiation is a necessity for a successful, modern, learning environment that meets the needs
of diverse learners. In their study recorded in Differentiated instruction enhances sixth-grade
students' mathematics self-efficacy, learning motives, and problem-solving skills (2020)
researchers Lai, Zhang, and Chang proved how differentiation in math is vital for student
success. Increased scores in mathematics self-efficacy (MSE), mathematics learning motives
(MLM), and mathematical problem-solving skills (MPSS) proved that differentiation increases
JOURNAL CRITIQUE: MATH AND THE DIFFERENTIATED CLASSROOM 6
References
King James Bible. (2023). King James Bible Online.
https://www.kingjamesbibleonline.org/ (Original work published in 1611)
Lai, C., Zhang, W., & Chang, Y. (2020). Differentiated instruction enhances sixth-grade
students'
mathematics self-efficacy, learning motives, and problem-solving skills. Social Behavior
and Personality, 48(6), 1-14. https://doi.org/10.2224/sbp.9094
Tomlinson, C. A. (2017). How to differentiate instruction in academically diverse
classrooms.
Association for Supervision & Curriculum Development
Urdan, T., & Midgley, C. (2003). Changes in the perceived classroom goal structure and
pattern
of adaptive learning during early adolescence. Contemporary Educational Psychology,
28, 524-551. https://doi.org/10.1016/S0361-476X(02)00060-7
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