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Supporting Struggling Learners in Mathematics
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Supporting Struggling Learners in Mathematics
Sometimes, despite our best efforts to provide best, first instruction, or simply due to the special needs of learners, students need additional support to learn mathematics. Before jumping to "Our students are struggling! What can we purchase to make it better!" you need to think more deeply about what the source of the struggle is and how an intervention can be specifically targeted. A supplemental curricular program might be what students need, but maybe access to a skilled math interventionist, or other educator with specialized training or experience, is a better resource. The skills that these interventionists have aren't always the same ones you would expect from a teacher in Tier 1 instruction, and can include various approaches to assessing, providing instruction, and giving feedback designed to help students who struggle.
Recommendations from the What Works Clearinghouse
In March of 2021, the What Works Clearinghouse updated its educator practice guide, Assisting Students Struggling with Mathematics: Intervention in the Elementary Grades. That guide contains the following six recommendations:
1. Systematic Instruction. Educators should provide systematic instruction during intervention to develop student understanding of mathematical ideas, including:
- Review and integrate previously learned content throughout intervention to ensure that students maintain understanding of concepts and procedures.
- When introducing new concepts and procedures, use accessible numbers to support learning.
- Sequence instruction so that the mathematics students are learning builds incrementally.
- Provide visual and verbal supports.
- Provide immediate, supportive feedback to students to address any misunderstandings.
2. Mathematical Language. Teach clear and concise mathematical language and support students’ use of language to help students effectively communicate their understanding of mathematical concepts, including:
- Routinely teach mathematical vocabulary to build students’ understanding of the mathematics they are learning.
- Use clear, concise, and correct mathematical language throughout lessons to reinforce students’ understanding of important mathematical vocabulary words.
- Support students in using mathematically precise language during their verbal and written explanations of their problem solving.
3. Representations. Use a well-chosen set of concrete and semi-concrete representations to support students’ learning of mathematical concepts and procedures, including:
- Provide students with the concrete and semi-concrete representations that effectively represent the concept or procedure being covered.
- When teaching concepts and procedures, connect concrete and semi-concrete representations to abstract representations.
- Provide ample and meaningful opportunities for students to use representations to help solidify the use of representations as “thinking tools.”
- Revisit concrete and semi-concrete representations periodically to reinforce and deepen understanding of mathematical ideas.
4. Number Lines. Use the number line to facilitate the learning of mathematical concepts and procedures, build understanding of grade-level material, and prepare students for advanced mathematics, including:
- Represent whole numbers, fractions, and decimals on a number line to build students’ understanding of numerical magnitude.
- Compare numbers and determine their relative magnitude using a number line to help students understand quantity.
- Use the number line to build students’ understanding of the concepts underlying operations.
5. Word Problems. Provide deliberate instruction on word problems to deepen students’ mathematical understanding and support their capacity to apply mathematical ideas.
- Teach students to identify word problem types that include the same type of action or event.
- Teach students a solution method for solving each problem type.
- Expand students’ ability to identify relevant information in word problems by presenting problem information differently.
- Teach vocabulary or language often used in word problems to help students understand the problem.
- Include a mix of previously and newly learned problem types throughout intervention.
6. Timed Activities. Regularly include timed activities as one way to build students’ fluency in mathematics.
- Identify already-learned topics for activities to support fluency and create a timeline.
- Choose the activity and accompanying materials to use in the timed activity and set clear expectations.
- Ensure that students have an efficient strategy to use as they complete the timed activity.
- Encourage and motivate students to work hard by having them chart their progress.
- Provide immediate feedback by asking students to correct errors using an efficient strategy.
Trusted Sources of Intervention Strategies and Materials
The internet is full of sites claiming to have math intervention resources and it can be difficult to know what claims to believe. Here are two sources that should be trustworthy:
The National Center on Intensive Intervention at American Institutes for Research (AIR) evaluates research on academic intervention programs based on the qualities of the studies. (Note: This is not the same thing as evaluating the programs themselves!) They include information and ratings on the technical rigor of a study's (a) quality of design and results, (b) quality of other indicators, (c) intensity, and (d) additional research. Their Academic Intervention Tools Chart can be filtered to show just those intervention tools that relate to mathematics and scanned to identify those with the most convincing evidence of their effectiveness.
The Evidence-Based Intervention Network (EBI Network), currently housed at the University of Missouri, is a collaboration involving researchers from universities across the country. They have had a math focus since 2013, and their site categorizes math interventions as (a) acquisition (the task is too hard for the student), (b) proficiency (the student needs fluency), (c) generalization (the student hasn't done the task that way before), and motivation (the student doesn't want to do the task). Within each category, interventions are listed with full intervention briefs describing the function of the intervention, the setting, alignment to standards domains, procedures, critical assumptions, materials, and supporting research.
In addition, the following resources might be helpful:
- The Colorado English Language Proficiency Standards provide Colorado educators with an invaluable resource for working with not only English Language Learners in mathematics but developing mathematical language in all students. The Can Do descriptors are a particularly helpful entry point to the standards.
- Open access mathematics materials for emerging bilingual learners of English, released by Understanding Language, were developed using research-based principles for designing mathematics instructional materials and tasks from two publicly accessible curriculum projects, Inside Mathematics and the Mathematics Assessment Project. Each lesson supports students in learning to communicate about a mathematical problem they have solved, to read and understand word problems, or to incorporate mathematical vocabulary in a problem-solving activity.
Wait! Why are some of the strategies here contradictory to what we see elsewhere about good math teaching?
For educators familiar with current trends in mathematics education, it can be alarming to see recommendations that contain things like timed activities or teaching vocabulary used in word problems. Weren't we told that timed activities are bad? And that keyword strategies or word walls for word problems are bad, too? Here are two tips to keep in mind:
- Read and study intervention strategies for nuance and avoid false dichotomies. You might still find fundamental differences in different recommendations, but if you go to the source, you'll find that recommendations come with considerations, prerequisites, and cautions. The "timed activities" recommendation from the WWC is a good example. In no way are those authors saying mad minutes and class-long flash card exercises are what your students need.
- Understand differences in perspective. A lot of influential work in mathematics education has been influenced by sociocultural perspectives on learning. In special education, researchers tend to take cognitive perspectives on learning. Neither perspective is right or wrong, but they're good at explaining different things. As a result, sometimes we get different recommendations from different sources, and that's something professional educators have to understand as the knowledge of our field sharpens and expands.