All students can build mastery in mathematics when the conditions are right. Access to excellent math instruction for all students creates opportunities for higher learning and ultimately better lives. For students to be successful in learning math, they must demonstrate reasoning and sense-making of math concepts.
Specifically, all students need to demonstrate success in algebra in order to open pathways into college and careers. If algebra is the gatekeeper to future success, we can open this gate by teaching mathematics through the lens of Universal Design for Learning (UDL). UDL is a framework that provides students with opportunities to work toward firm goals through flexible means.
When used in mathematics classrooms, UDL helps minimize barriers that prevent students from seeing themselves as capable problem-solvers with agency as mathematicians. For students to reach their full potential as “math people,” all learners must participate in meaningful, challenging learning opportunities.
3 Steps to Increasing Accessibility
1. Determine high-priority concepts in each grade. All students deserve access to rigorous math learning opportunities at their grade level. Students are often unintentionally excluded from grade-level instruction to focus on misconceptions or missed learning opportunities from previous grade levels, making it nearly impossible for them to engage in challenging problem-solving and sense-making opportunities with their peers.
All Learners Network, an organization Ashley is part of that promotes math equity and inclusion for all students, identifies high leverage concepts (HLCs) at each grade level. These are the key mathematical understandings that all students need in order to engage with grade-level content the following year. These concepts build toward understanding of algebra, supporting successful learning of mathematics to prepare for college and career readiness. HLCs are the focus of most Tier 2 (small group) and Tier 3 (individualized) interventions at a particular grade level.
2. Provide scaffolding. An individual student may also need additional scaffolding related to the HLCs to engage in an inquiry-based learning opportunity on grade-level content. When planning math instruction, teachers should consider the priority concepts from previous grade levels that support their current learning objectives and consider scaffolds that students may need in order to participate in grade-level learning.
Numerous scaffolds make math instruction more accessible for all learners. The key is providing scaffolds as options for instruction and not one-size-fits-all solutions. Share available scaffolds, and ask students to reflect and determine which tools they need so they are both supported and challenged.
Conceptual scaffolds: These may include manipulatives, calculators, exemplars of done problems, and solution keys. For example, a sixth-grade student working on solving a problem on unit rates may benefit from using a calculator to calculate single-digit multiplication problems, so that their brainpower is dedicated to more complex reasoning.
Sociocultural scaffolds: These include options for students to work in pairs or small groups, options for conferencing with the teacher for targeted feedback, and options to revise and resubmit work as they work toward mastery.
Linguistic scaffolds: Mathematics curriculum often creates barriers for students who struggle with literacy. There are concrete linguistic scaffolds that teachers can implement to reduce linguistic demands. When planning instruction, be sure that text is accessible to all learners, including multilingual learners and students with disabilities. For example, word problems require that students read and comprehend the text of the problem and identify the question that needs to be answered before they can create and solve an equation.
Teachers can leverage technology by creating an audio file of the text, and/or providing text digitally so that students can use read-aloud and translation tools. Teachers can use low-tech options as well by choral-reading the problem, asking students to discuss the key information in the problem and clarifying vocabulary, brainstorming what the answer might look like, and estimating before solving.
Teachers may also provide students with word banks with simple definitions, creating visual representations of word problems. For example, a problem that begins with “A student earns $12 each time he shovels his neighbor’s driveway. He earned a total of $108 shoveling the driveway last winter” could be paired with an image of a student shoveling a snowy driveway with a snow shovel. This allows students who struggle with comprehension, or students who have never experienced a snowy winter, to visualize the context so that they can use their brainpower to solve the problem.
3. Embrace the power of problem-solving. Problem-solving asks students to solve, analyze, prove, and critique, all of which are much more complex forms of thinking than memorize, apply, repeat, or recall. For students to become expert mathematicians, they need opportunities to make sense of problems, persevere in solving them, represent their thinking through flexible means, and compare and contrast their reasoning with the reasoning of others. These standards of mathematical practice describe the level of expertise that all students need in order to productively struggle through a problem. Thinking is necessary for students to learn mathematics, and they need access to quality tasks with rich math content using the abovementioned scaffolds in order to engage in this deep thinking.
Teachers can create a classroom that embraces problem-solving by minimizing a focus on getting things right the first time and avoiding traditional grading practices where getting the correct answer is more important than the process. For instance, the teacher might ask questions like the following:
- “Jenna got the answer for this problem. How do you think she got the answer?”
- “How many different strategies can you use to solve this problem? Which strategy is the most efficient?”
- “How is Martine’s idea like Jenna’s?”
For the prompts above, students may respond with the following:
- “Jenna solved the problem by drawing a number line and counting up 5 jumps starting at 98 and going to 103.”
- “I counted back from 103 to 98 and counted up to 103 from 98. I think counting up was more efficient because I could just count on my fingers and didn’t have to count back.”
- “Martine’s idea is like Jenna’s because Martine counted up on a number line and Jenna counted up on her fingers.”
When students have opportunities to think, reason, explain, and model their thinking, they are more readily able to develop a deep understanding of mathematics beyond rote memorization. The goal is for all students to experience success in higher learning of mathematics—requiring those reasoning and sense-making skills and increasing engagement.
A lack of engagement is a barrier to learning. Students need to feel that the learning opportunities provided for them are authentic, relevant, and rigorous. When teachers believe that all students can achieve high levels of mathematics, students will rise to that challenge.