Strategies for solving multiplicative problems using a conceptual model-based problem-solving approach. A case study with a student with autism spectrum disorder



Multiplication: a cornerstone of math, a source of frustration for some students. For students with Autism Spectrum Disorder (ASD), mastering multiplication can present a unique set of challenges. Traditional methods that rely on memorizing formulas and procedures can leave them struggling with abstract concepts.


A recent study published in April 2024 sheds light on a promising approach to bridge this gap: the Conceptual Model-based Problem-Solving (COMPS) approach. This blog post delves deeper into the research, exploring the challenges faced by students with ASD, the core principles of COMPS, and its potential benefits.


Understanding the Roadblocks: Multiplication and ASD


The study, titled “Strategies for solving multiplicative problems using a conceptual model-based problem-solving approach. A case study with a student with autism spectrum disorder,” acknowledges the difficulties students with ASD encounter when tackling word problems involving multiplication.


Rote memorization, a mainstay of traditional methods, often proves ineffective for students with ASD. This research suggests that relying solely on memorizing formulas can hinder their ability to grasp the fundamental logic behind multiplication. Without a strong conceptual understanding, students struggle to apply their knowledge to new situations, leading to frustration and a sense of being lost.


Enter COMPS: The Power of Visuals in Multiplication


The COMPS approach offers a refreshing alternative. It introduces visual models, or diagrams, specifically designed to represent the relationships between numbers in various multiplication problems. These problems typically fall into three categories:

  • Equal-groups problems: Imagine rows of cupcakes on baking trays. If there are X cupcakes on each tray and Y trays in total, how many cupcakes are there altogether?
  • Multiplicative comparison problems: If John has W times more apples than Sarah, and Sarah has Z apples, how many apples does John have?
  • Combination problems: A clothing store has A different types of shirts and B colors. How many total shirt combinations are available?


By using diagrams specifically tailored to each problem type, COMPS helps students visualize the multiplication concept. This visual representation acts as a bridge, connecting the abstract world of word problems to the concrete actions of multiplication.


For instance, in an equal-groups problem, the diagram might depict rows of circles representing cupcakes, with the number of circles in each row and the total number of rows clearly marked. This allows students to see multiplication not just as an operation with numbers, but as a process of repeatedly adding equal groups.


A Case Study in Action: Unveiling the Impact of COMPS


The research employs a case study, focusing on a 14-year-old student with ASD and intellectual disabilities. The study investigates how the student’s problem-solving strategies and conceptual understanding of multiplication evolve through COMPS instruction.


The researchers meticulously analyze the student’s performance before and after implementing the COMPS approach. They observe significant changes in the student’s ability to:

  • Identify the correct operation: The student demonstrates a newfound ability to differentiate between multiplication and division based on the problem type represented by the visual model.
  • Solve word problems accurately: Equipped with a deeper understanding, the student achieves greater success in solving multiplication word problems.
  • Explain reasoning behind solutions: The student can not only arrive at the correct answer but also explain the thought process behind their solution, showcasing a grasp of the underlying concepts.


A Glimpse into the Future: The Potential of COMPS


This research offers a compelling argument for the potential of the COMPS approach in enhancing multiplication skills for students with ASD. By leveraging visual models, COMPS fosters a deeper understanding of the concept, going beyond rote memorization and building a strong foundation for future mathematical learning.


While further research with a larger sample size is necessary to solidify the effectiveness of COMPS, this initial study provides valuable insights for educators seeking alternative methods to teach multiplication to students with ASD. By incorporating visuals and building a strong conceptual foundation, educators can empower students with ASD to not just solve multiplication problems, but to truly conquer the multiplication challenge.


The impact of COMPS extends beyond the classroom. By fostering a sense of accomplishment and building confidence in their mathematical abilities, the COMPS approach can empower students with ASD to approach new learning experiences with a more positive outlook.



Does COMPS replace traditional multiplication methods altogether?

The research suggests that COMPS should be used as a complementary approach, not a replacement for traditional methods. Traditional methods can still be valuable once a strong conceptual understanding is established through COMPS. COMPS equips students with a deeper understanding, allowing them to approach traditional methods with greater confidence and efficiency.


Is COMPS beneficial for all students with ASD?

The current research is based on a case study of one student. While the results are promising, further studies with a larger and more diverse group of students with ASD are needed to determine the generalizability of the COMPS approach. However, the focus on visuals aligns well with the strengths of many students with ASD, suggesting its potential effectiveness for a wider population.


Can COMPS be adapted for other mathematical concepts besides multiplication?

The core principles of COMPS, such as using visual models to represent mathematical relationships, can potentially be adapted to other mathematical concepts. Further research is needed to explore how COMPS can be applied to other areas of mathematics, but the potential for broader application is certainly there.


How can parents get involved in supporting their child’s learning with COMPS?

Parents can play a crucial role in supporting their child’s learning with COMPS. By familiarizing themselves with the visual models used in COMPS, parents can engage with their child’s learning at home. Practicing problems together and discussing the visual representations can reinforce the concepts learned in school.


What are some of the challenges educators might face when implementing COMPS?

One challenge educators might face is the time investment required to create and incorporate COMPS materials into their lessons. Additionally, some educators may require professional development to become familiar with the COMPS approach and feel comfortable using it effectively in the classroom.



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