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The study, Mathematics Instruction for Students with Learning Disabilities: A Meta-
Analysis of Instructional Components (Gersten et al., 2009) assessed the findings of forty-two
interventional studies/trials on instructional strategies that claim to improve the mathematical
skills of students who have learning disabilities. Specific areas of struggle for students with
learning disabilities (LD) were also identified, chiefly word problems, concepts and procedures
involving rational numbers, and understanding of the properties of whole numbers such as
commutativity. The research then sought to evaluate, compare and rank the interventions
numerically based on the researchers’ four categories. By coding and ranking these methods
following the specific categories, the researchers were able to systematically evaluate the
effectiveness of specific instructional strategies on the most problematic areas for students with
learning disabilities.
The impact of four categories of instructional components was examined in the study: (a)
approaches to instruction and/or curriculum design, (b) formative assessment data and feedback
to teachers on students' mathematics performance, (c) formative data and feedback to students
with LD on their performance, and (d) peer-assisted mathematics instruction. All instructional
components, with the exception of student feedback with goal-setting and peer-assisted learning
within a class, yielded significant mean effects ranging from 0.21 to 1.56. Additionally, the
effectiveness of these components was assessed conditionally using hierarchical multiple
regressions, revealing that two instructional components—teaching students to use heuristics and
explicit instruction—resulted in practically and statistically important increases in effect size.
The study also delved into its limitations, proposed suggestions for future research, and
discussed applications for the improvement of current practice (Gersten et al., 2009).
Analysis
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The information in the study identifies and analyzes forty-two suggested math
interventions for students identified with learning disabilities. It is important to note that not all
studies reported information regarding specific participant information such as socioeconomic
status, gender, and race/ethnicity. This missing information could skew results of interventions
effectiveness for specific disabilities, genders, etc. (Gersten et al., 2009). The studies also did not
always isolate the individual strategy/intervention and many were used in conjunction with other
strategies (typically direct instruction). Armed with this knowledge, the researchers compiled a
table to evaluate the effectiveness of the strategies based on the scale created by the research
team. They also compiled a list of the most frequently used strategies and further expanded the
implementation and effectiveness of those strategies.
The strategies identified as the most used were explicit instruction, use of heuristics
(mental shortcuts), student verbalizations of their mathematical reasoning, visual representations
while problem solving, and providing feedback. Direct Instruction is one of the most frequently
researched instructional methods, with polarizing opinions regarding its effectiveness in the
classroom (Mason & Otero, 2021). The overwhelming evidence shows that direct instruction,
when properly scaffolded, is an effective method of teaching new information. Gersten et al.
showed similar patterns in their research, and when combined with an additional strategy, direct
instruction rated higher on the scale established by the researchers.
In mathematics, heuristics refers to problem-solving strategies or techniques that
individuals use to approach mathematical problems. These strategies often involve trial and
error, intuitive reasoning, and creative thinking rather than relying solely on formal mathematical
algorithms or procedures. Heuristics in mathematics can help students navigate complex
problems, explore different solution pathways, and develop a deeper understanding of
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mathematical concepts (Hänze & Leiss, 2022). This is reflected in the research presented by
Gersten et al.
Two of the techniques mentioned, of the five most effective, identified in the research
presented in Mathematics Instruction for Students with Learning Disabilities: A Meta-Analysis
of Instructional Components (Gersten et al., 2009) are common methods used in the classroom
setting. Verbalizing mathematical reasoning and visual representation while problem solving go
hand in hand. Students state their mathematical reasoning orally, allowing them to express
understanding or work out their thought process when solving the problem. Visual
representations of problem solving work in a similar way, allowing students to visualize abstract
mathematical processes. Visual representations play a vital role in problem-solving by providing
individuals with a tangible framework for understanding, analyzing, and solving complex
problems (Samosa et al., 2021).
Lastly there is feedback, both student and teacher. This feedback can come from informal
or formal assessments, self-reflection, etc. Feedback is a necessary tool for gathering data on
student success, student learning styles, interests, etc. Teachers should use this information to
adjust and plan lessons to ensure that the instructional methods/interventions chosen and
employed are the most effective for the diverse needs of the students. This is especially
important in mathematics education where higher-order solving skills are built upon foundational
mathematical practices.
Application
The practical application of the information gleaned from the study Mathematics
Instruction for Students with Learning Disabilities: A Meta-Analysis of Instructional
Components by Gersten et al. (2009) is multifaceted and directly applicable in the mathematics
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classroom. The most effective practices highlighted are elements of beneficial instructional
differentiation for mathematics education, both for neurotypical students and those identified as
having a learning disability. The data also showed the most important information for
implementing these strategies, that they are more effective combined than separately in the
classroom.
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References:
Gersten, R., Chard, D. J., Jayanthi, M., Baker, S. K., Morphy, P., & Flojo, J. (2009).
Mathematics Instruction for Students with Learning Disabilities: A Meta-Analysis of
Instructional Components. Review of Educational Research, 79(3), 1202–1242.
http://www.jstor.org/stable/40469093
Hänze, M. &, Leiss, D. (2022) Using heuristic worked examples to promote solving of
reality-based tasks in mathematics in lower secondary school. Instr Sci 50, 529–
549. https://doi.org/10.1007/s11251-022-09583-8
Mason, L., & Otero, M. (2021). Just How Effective is Direct Instruction?. Perspectives on
behavior science, 44(2-3), 225–244. https://doi.org/10.1007/s40614-021-00295-x
Samosa, R., Dominguez, J., Budaño, S., Ronquillo, C., & Yumul, R. (2021). Visualize,
represent and solve problem technique as teaching strategy to improve the learner’s
problem solving skill in Mathematics 2. International Journal of Academic
Multidisciplinary Research (IJAMR), 5(12), 75–78.
https://files.eric.ed.gov/fulltext/ED618220.pdf
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