Math can feel hard, and for good reason. Many of us grew up learning math as a race to memorize formulas and solve problems quickly, focusing on efficiency and repetition. It often felt disconnected from real life, tailored for a select group of students who would go onto careers that needed higher-level math. So it’s no surprise that for many parents of children with disabilities, math stands out as one of the toughest hurdles in making the general education curriculum truly accessible.
But math has come a long way since most parents were in school, as has our understanding of how disabilities can affect math learning. To understand how to help your child — both through the IEP process and through the individual support you might give during classwork and homework — it’s important to first understand how math is taught in California classrooms, how special education approaches math instruction, and what schools aim to teach your child during math instruction. In other words: what is the purpose of math?
To find out what parents need to know — and should be asking — about math, we sat down with two special education mathematics experts: Sarah Noland, special education math specialist at Calvert County Public Schools and Rachel Lambert, PhD, associate professor in Special Education and Mathematics Education at UCSB and author of Rethinking Disability and Mathematics.
Special education in math is a problem — mostly because it's not working. More than a decade after the Common Core overhaul of math education in the US, children with disabilities continue to struggle in math. Many students with significant cognitive disabilities are offered a “functional math” curriculum and goals that emphasize outdated skills, such as recognizing and counting coins, which are rarely used in daily life, or reading analog clocks that don’t even exist in their schools. Find more on math goals in our article here.
What does the data show?
National Assessment of Educational Progress (NAEP) tests provide a snapshot of educational success across the US. The results show that a decade of Common Core math has not significantly changed the ability of students to pass these tests. For students with disabilities, the gap has actually widened. In 2019, only 7% of 12th graders with disabilities and 17% of 4th graders with disabilities were proficient in math. Similarly, only 50% of students with disabilities achieved scores at the basic level in 4th grade (compared to 59% in 2009, before the introduction of Common Core). It’s also worth noting that the NAEP testing leaves out many students with disabilities whose needs cannot be accommodated in the test. In California, we see a similar gap in our state testing. In the 2022-23 school year, only 12.26% of students with disabilities met or exceeded the state standard for math. Only 8.86% of students with significant cognitive disabilities met level 3 (demonstrating understanding) for math in the California Alternate Assessment.
For many parents with kids with complex needs, especially those in high school, math is often the most difficult curriculum to access. As a result, math expectations can become significant barriers to achieving success — whether that’s earning a high school diploma, pursuing college, or securing a job. Special education experts are rethinking math teaching, but in the meantime, how do we as parents help our children not only survive but also thrive in math?
Studies have shown that many students (with and without disabilities) suffer from math anxiety, and this is strongly related to using rote memorization as a learning strategy in math. Professor Jo Boaler of Stanford University, one of the architects of the California Math Framework, stresses the need to avoid ways of teaching math that can leave adults believing that they are “not math people.”
Research also reveals that math anxiety is passed on to children by teachers and parents. One study found that the amount of math anxiety expressed by parents predicted their child’s math achievement in school. “The amount of math knowledge parents had was not important, only how anxious they were. And their math anxiety only impacted students negatively if parents helped with homework. This suggests that math anxiety is passed on to children when parents (and teachers) are having conversations with them about mathematics.”
Dr. Lambert explains how the move away from rote memorization and speed tests also makes math more accessible to more people, especially students with disabilities.
Before we explore more, let’s decode these math standards. Common Core State Standards (CCSS), Standards of Mathematical Practice (SMPs), Mathematics Framework — it sounds like a lot, and it’s okay if you still haven’t quite figured out how they work together. The California CCSS in math actually includes two types of standards: eight Standards of Mathematical Practice (SMPs) (identical for each grade level) and mathematical content standards (different at each grade level). Think of it like this: mathematical content standards identify what you learn in math (the big ideas, mathematical skills, and content) and the SMPs focus on how you do math.
Side note: in California, we also have the Mathematics Framework, introduced in 2013, which provides guidance to schools about how to implement the CCSS. Think of this as when you do the math. This sets out the pathways for high school, where some schools will do the traditional pathway: Algebra I, Geometry, Algebra II and others will offer the integrated pathway: Mathematics I, II, and III. Schools also offer advanced classes such as Pre-Calculus, Statistics or Data Science, and Calculus. The California Mathematics Framework was revised in 2023 and will be introduced in schools over the next few years, providing guidance on the CCSS curriculum at each grade level.
In kindergarten through grade 8, the California state standards are organized by grade level and then by domains — clusters of standards that address “big ideas” and support connections of topics across the grades (in high school they are organized slightly differently using concept categories). The clusters are groups of related standards that tell us what students should understand and be able to do. The standards do not dictate curriculum or pedagogy, only what students are expected to learn.
So, for example, the CCSS 2.NBT 1a.
Understand place value: Understanding 100 can be thought of as a bundle of ten tens—called a “hundred.”
A child could be working on this very specific idea as their targeted math skill. However, for a child who is not able to match numbers 1 through 5 with objects, this state standard will likely be overly ambitious. But the domain — or “big idea,” which is in this case place value — could be taught just by focusing on the number 10. At the same time, you could take any of the SMPs and apply them to a student working on subitizing 1 to 5, even if their units are tens or bundles of ten. They might be looking for a pattern (four of something) or attending to precision (getting the right number) or making sense of numbers 1 to 5.
For more information on the CCSS Big Ideas in Math, K-8, grab our downloadable pdf here!
Let’s untangle the SMPs and their importance in math learning. The SMPs are distinct from the content standards for each grade level. The CCSS content standards identify the big ideas, mathematical skills, and content to be taught. The SMPs focus on how you do math, while the content standards focus on what children learn in math, such as addition, multiplication, and fractions. The SMPs are the same for all grade levels and can be applied whether you are learning to count or doing calculus.
SMPs provide guidance for how we do math, whether we are mathematicians or elementary students. And while the SMPs each have a unique focus, they work together when put into practice. The impact of the SMPs is to make math much more about how we solve problems and less about “getting the answer right.” Like the professional mathematicians who collaborate and communicate using visual models and mathematical language, the SMPs add a lot of communication practice into the math classroom. This isn't a side benefit of math — communication is actually part of doing math.
Both Noland and Dr. Lambert see the Common Core Standards for Mathematical Practice (SMPs) as pivotal in how we teach math — in general and to students with disabilities.
Listen to Dr. Lambert explain why the SMPs are so important to teaching math in special education:
For Noland, the new approach to math is about engaging students and thinking about how students can communicate where they are in their learning progression. She tells us, “Over the years, we've had this shift where we're really spending a lot of time with our learners talking about conceptual understanding, building strategy, instruction, and the use of tools. There’s this learning that we have to engage with — educators, parents, and just the community overall — to understand that we’re not in a place anymore where it’s just about memorization, and we really need to make sure that when we are providing specially designed instruction, that really speaks to ‘What are the goals? What are the accommodations, supplementary aids, and services? How are we taking the current lesson and really planning for the individual needs of that learner?’ We have to think about math as a bigger picture and not these little isolated discrete skills that we’re looking at.”
SMPs also make math accessible. Noland explains that the SMPs are pivotal in making math accessible to all students, especially in an inclusive general education setting. Often, math class can be a great place to learn more general skills that we see within the SMPs.
Explicit instruction or inquiry-based learning?
As far back as the 1960s, many educators developed an approach to math (for all children) that was rooted in the child’s natural curiosity about the world. This approach focused on presenting problems that could be solved with mathematical thinking and encouraging children to work collaboratively to solve the problem and develop their own strategic thinking.
Inquiry-based learning
The introduction of the Common Core State Standards (CCSS) in 2011 enshrined this approach — now termed “inquiry.” Rather than teaching kids a single approach to solving problems and having them memorize it by repetition, teachers engage students in mathematical problem solving with supports to help students make sense of the problem and communicate their thinking. Students can explore multiple strategies, although they don't need to become experts in all of them.
The focus of the Common Core was not just on introducing new ways to work out problems but on using the inquiry method of teaching to develop independence in critical thinking and problem-solving. The educationalists wanted children to learn to behave more like professional mathematicians do when solving problems. It turns out that professional mathematicians solve problems mostly collaboratively. They can explain the problem, their solution, and where they’re stuck using mathematical language, then demonstrate it by often drawing the problem out through visual and spatial thinking.
This approach led to the incorporation of eight Standards of Mathematical Practice in the Common Core State Standards. These standards stand alongside and support the grade-level content standards (such as solving multiplication and division problems in third grade).
Since this new way of teaching was introduced over a decade ago, there is a growing concern that inquiry-based teaching is not supporting students with disabilities. The Science of Math, for example, is a concept growing in popularity with special educators that emphasizes the use of evidence-based practices in math. The Science of Math advocates for students with disabilities (and other kids who struggle with math) to receive explicit instruction to develop the basic math skills needed to participate in project-based and exploratory math learning. On the other hand, many math classrooms are still not implementing inquiry-based teaching with fidelity. Our experts emphasised making math relevant to real world situations, making it visual and concrete as more impactful for students with disabilities than drilling students with foundational math skills.
Is blending the best option?
Often, teachers approach math solely with a problem-solving approach, leaving the students to make their own inferences from the exercise. This isn’t sufficient for many students with disabilities. At the same time, many separate special education classrooms have not updated their math curricula to reflect the Common Core approach and language utilized in the tests. Their focus is only on explicit instruction in basic skills that often don’t fit with the expectations of the CCSS general education curriculum. Since the goal of special education is to provide access to the curriculum, focusing on discrete skills is not always closing the gap. It’s also important to remember that many special education teachers have had little training in teaching math and may have been excluded from professional development as CCSS was introduced.
But both approaches can be used together. Dr. Lambert proposes a blending of both instructional methods called Guided Inquiry, a method of teaching math that uses both inquiry strategies and explicit instruction for learning. Her method incorporates Universal Design for Learning and focuses on making math meaningful for all students.
So many kids with extensive support needs, especially those in separate classes, seem to get stuck on basic addition and subtraction and never move on to multiplication, fractions, or other interesting topics, such as sets or graphing.
In Dr. Lambert’s experience, it’s important not to get stuck in a single level of math learning. “I’ve seen a lot of kids who can do higher mathematics but can’t count accurately. As parents, we need to understand that math is not a ladder where they have to understand every single thing before they move on. It is not. A better metaphor is that math is a house, and some walls are load-bearing and some walls are not.” For example, things like number sense and understanding how digits work (like place value) in a meaningful way is a “load-bearing wall” because kids can’t know how numbers are bigger or smaller without that. “But we have to figure out what really matters and what we can put to the side because we’re going to keep building this house.”
Noland agrees that while students need foundational skills, too often students with disabilities spend their entire educational career working on basic one-to-one correspondence, often missing opportunities to learn about graphing, for example. A student might have a strength for seeing things visually when presented in a graph or engaging in probability scores or certain geometry concepts. While foundational skills like counting, making sense, decomposing, composing, and subitizing are important, Noland tells us that the other part of math learning should be in “experiencing the other great ideas that are in math.”
The question for many parents presented with goals for high school and transition that involve analog clocks and identifying coins: are these really the load-bearing walls? If not, then how do we identify the skills that will be pivotal in accessing the curriculum later in the child’s education?
Asynchronous development is common in both children with disabilities and gifted children. Dr. Lambert unpacks some of the common skills and debunks the myth that they must be mastered in order.
Counting. Many children with short-term memory issues find counting very difficult to master. Dr. Lambert breaks it into different skills and demonstrates that not everyone learns these in order: counting in sequence, one to one correspondence and cardinality. These skills can be practiced and taught using different strategies to engage kids.
Children who have trouble with counting because they find it difficult to remember the order of numbers can be given a visual, such as a number line. Lambert uses counting collections (such as lego) as a way to engage kids in everyday math.
Go forth and multiply. Multiplying is an important skill in everyday life; it is used for such tasks as setting the table, doubling a recipe, charging the correct amount for a purchase of multiple items, etc. We asked our experts about the transition to multiplication and determining the appropriate readiness of children.
Dr. Lambert tells us that a lot of kids find multiplication, generally first introduced in the third grade, easier than the multi-digit subtraction that kids often do in second grade, mostly because multiplication can be very visual for kids. For example, kids might build towers of blocks to show three sets of four. She tells us, “Subtraction is particularly challenging. But what happens to kids is that when they get stuck, if they don't pass this goal, they’re never going to move past subtraction. They’re going to be subtracting for the rest of their lives. That’s not a good idea. That’s when I put the calculator in place and then move on to something that could be fresh and new and different.”
Two skills stand out as pivotal or ‘supporting walls’. Multiplication is an operation that is frequently used in pre-algebra and algebra. Proficiency with fractions is another skill that is predictive of success in middle and high school math. These are both high-leverage skills that can be prioritized and also might be embedded and practiced by students not able to work on grade level.
Fractions will take you to space! There is evidence that fractions are critical for understanding algebra. Many students that are “behind” in math are still mastering skills in basic computation when fractions are introduced. However, fractions are a big idea that is used in everyday life (like slices of pizza) in money and also help when students get to high school math. There are many visual and tactile ways to teach fractions, even for children with limited number sense.
What the heck is number sense? Number sense, which includes place value, is a big idea that includes a lot of math skills. Together, they help us make sense of math problems. For example, understanding more and less, larger and smaller, or greater than and less than; understanding quantities through counting objects; making sets and subitizing; and understanding cardinality — the order of numbers, such as first, second, and third. Place value helps us understand the number system and manipulate large numbers.
In her book, Dr. Lambert says, “Number sense and place value are definitely load-bearing walls for the rest of mathematics — in other words, these ideas about numbers and the number system are core mathematical ideas that are worthy of significant investment.”
Dr. Lambert recommends choral counting and counting collections as great ways to practice number sense.
The concept of “functional” math is often used to describe an alternative curriculum for students with significant cognitive disabilities or math goals that diverge from the grade-level standards. There is no clear definition of “functional math.” Unpacking the distinction opens an ableist can of worms.
Students with intellectual disabilities who struggle with math even at a basic level, such as counting to 20, are diverted to a curriculum of math concepts that might come up in their adult lives. This, of course, assumes that their adult life will not include college or any workplace that will require secondary school math. It assumes they will not be earning enough money to worry about compound interest. They are assumed to be devoid of interest in civics, which might require a basic understanding of statistics. It assumes that they need to understand how to tell time using a clock so they know what time to start work, finish work, and go to bed. It assumes that they’ll need to recognize coins because they will exist in a cash economy earning pennies on the dollar. This is a math curriculum designed for adults whose futures are being limited for them, but we want (and need) our education system to dream bigger for our kids.
Instead, we can assume that our children might grow into adults who will use apps to take rides, apps that are funded by a bank account filled by wage they earn at a job they find purposeful and enjoy, within a diverse community, or funded by benefits they can independently manage, and rides that take them to fun places in their diverse community, such as museums and concerts, and to a home of their own, with people of their choosing, who make their own food. What kind of math will our children need to live in this adult life that we envision for them? They will need the ability to make sense of numbers; solve problems like tipping, paying rent, and checking their pay stub; and communicate their solutions and collaborate effectively with others to get help. For some these skills will be in a context of interdependence, utilizing significant support, but we still want the student to have a functional understanding of what is happening so they can have ownership of the process.
Rethinking functional math — math is all around us
So how should we teach kids this functional math — math that will actually prepare them for a rewarding life in our current society? Math that is taught in an engaging way, related to the real world, teaches children how to solve problems. For both Noland and Dr. Lambert, all math has to be related to the child’s life. Dr. Lambert says, “You should be counting what they care about.… It all needs to be made super relevant, really visual, and really accessible to kids.” For example, kids might be motivated to count the number of Legos they have, or their cars, or stickers — for each kid, this can be a different solution.
Dr. Lambert explains that functional mathematics should be understood in a way that connects to the world of children. She explains that good math instruction for young children starts with pulling out the mathematics that make sense to them and beginning there. “I advocate very much for kids to get mathematics that begin in the concrete and the sense-making and what’s really happening in the real world. That's how all children should begin, and it shouldn’t be something separate.”
This is even more vital for children with disabilities.
Bringing functional math to the present
Functional math is often understood in a pretty old-fashioned way. As mentioned, goals often focus on identifying coins and telling time on analog clocks, which you can hardly find in a classroom nowadays. Dr. Lambert tells us, “We need to think about how money connects in a time of credit cards, when we’re paying with our phones. What do kids need? They need to be able to estimate how big a number is; they need a strong number sense because they need to know if they have enough money in their bank account to pay for it. This number is smaller than this number. Counting with money might be less relevant than it used to be, although it is a wonderful way to teach place value. So money is a wonderful tool to teach other math concepts.”
Noland adds that “functional math” can actually be different for each individual student but should always be meaningful to their lives: “When I think about functional math, my brain defaults to that thinking that I have to teach them counting coins or time to the hour. But again, if I think about what is truly functional math, it is functioning within our world, which is math. I talk to kids all the time who say, ‘I hate math. I hate math.’ I say, ‘Sorry, kids, life is math, math is life. You can’t get away from it no matter what you do. So you might as well make sense of it.’ And maybe it’s individual. But I think it is all functional. We just need to stop saying ‘functional’ and instead focus on the math skills that the student needs to develop so that they can be a stronger member of the community, or the skills that the student needs that will lead to independence.”
Calculators can be a great tool for students who struggle with basic math facts. How and when to introduce the use of a calculator can be a common dilemma for IEP teams. It’s important to consider the overall objective in using the calculator. Dr. Lambert says, “In any math topic, I would always make sure that my child is beginning in sense-making. Is what they’re doing concrete? Does it make sense to them? Does it feel real?”
Using a calculator is not sense-making. As Dr. Lambert continues, “When a child is learning how to add and subtract small numbers, they need to learn through concrete manipulatives and putting blocks together before it becomes abstract. The calculator should not be the first tool because a calculator is abstract — you just punch in the digits. Learning addition, subtraction, multiplication, and division should be real, visual, and tangible for kids first, then gradually become more abstract. Once they can do a problem just with the numbers, that’s when you can transition to a calculator if they need it.”
A calculator is not a replacement for teaching foundational math skills. It can also be an essential tool for students.
Some IEP teams might delay the use of a calculator to give students continued time on that normal sort of progression of building fluency with single digits. However, for some students with disabilities, we need to consider using tools that reduce the barrier. “We’re leveling the playing field for the student to engage in grade-level math with the tools,” Noland says. We need to think about how we are building the capacity of the student to use resources rather than telling them they have to know the algorithm.
When is the timing right to introduce a calculator?
Timing for introducing the calculator should depend on the student’s ability, but there may be some regulations depending on your state about the use of a calculator as an accommodation in statewide testing. If your IEP team is reluctant to introduce a calculator, ensure that other tools are considered, such as a number line, fraction bars, connect counters, a hundreds chart, an addition chart, or a multiplication table. Make sure these tools are written in as accommodations in the IEP, your child is taught how to use them, and the tools are provided in every math class.
Noland goes on to say, “Starting at the end of fourth grade is when the calculator becomes pivotal, because again, it’s about leveling the playing field. And if we get into fourth grade and we’re looking at standards — that they have to multiply multi-digit numbers, they have to divide, they have to multiply decimals — if their access and their tool to meet that standard is going to be through the use of a calculator, I think that’s okay.”
Don’t fear the calculator
Noland adds that calculators are very important in a child’s educational journey. It’s important for most students to start working with the calculator in fourth grade because it gets them proficient with it. Students will continue to use that calculator in middle school. It can be particularly difficult for a middle school student to learn to use the calculator, having never used it, and follow along with grade-level work.
She adds, “I think the calculator plays a very integral role for many of our students to allow them to progress and make access in the general life curriculum, and to allow them to be really a member of the full math community. Because that is a real-life tool, so I don’t want parents to be afraid of the calculator.” Beyond just a calculator, there are so many other ways we can use technology, tools, and apps to make learning math easier and more engaging. For more resources, head to our article Math Curriculum Materials, Tech, Apps, and More! Where we explore math programs, curricula, websites, assistive technology, tools, and apps to support your child in reaching their math goals.
In high school, math becomes a little intimidating for many parents. For many of us, algebra was not taught in a way that showed us its relevance to everyday life. Our notion of algebra involves a lot of memorization and not much engagement. For many parents of children with cognitive disabilities, this is the point at which it makes sense to depart from the curriculum and set goals that focus more on basic math skills. According to Dr. Lambert, however, algebra can open the door to useful learning experiences no matter what level the child is at. She explains that it really depends on how algebra is taught.
While Algebra I is still a state requirement for a diploma (even the alternate pathway to a diploma), the California Math Framework points toward the trend to replace Algebra II with data science, in part because it’s easier to see the everyday uses of data science in the world outside education. Dr. Lambert says that’s something to think about for all kids: “I do love algebra, but I think understanding how data is being used, and statistics, and understanding charts and graphs in a real meaningful way, making those charts and graphs, can be really wonderful mathematics for kids.”
For more information, head to our article Accessible Algebra for EVERY Learner.
Dyscalculia is a specific learning disability that affects educational progress in math. Dr. Lambert tells us that often we think about it as a difficulty with the symbolic nature of mathematics — not just the digits, but math symbols such as the plus or minus sign. People with dyscalculia also often have trouble with computation and might need the support of a calculator for fluency in computation, for example, but can still engage in grade-level mathematics.
Much of the recent research on supporting students with dyscalculia may also help students with other developmental disabilities, such as Down syndrome, as researchers understand better why some brain differences present difficulties working with numbers.
Dr. Lambert says that people with dyscalculia need visuals and manipulatives to make sense of math: “It needs to be real world, and the minute we make it abstract, that’s when we’re making it almost impossible for them to engage. If we think about Universal Design for Learning, we’re supporting all kids if we say, ‘Okay, it’s fifth grade, we’re solving a problem, we have different ways: there’s a calculator, there’s paper, there’s blocks — do what you need to do. Work alone if you need to, work with others, do what makes sense to you because we want to make sure that everybody has access to what makes sense to them. Because for dyscalculia, it often means going back to the concrete, making sure they understand it before they can go forward.” Read more in our article Dyscalculia 101.
Like we said in the beginning: math is hard! But math can be important simply because of how hard some people find it. Dr. Lambert says that math teaches perseverance, the ability to keep doing something in spite of obstacles. “Everybody gets stuck in mathematics, including mathematicians. What do you do when you’re stuck?” She says it’s not about feeding kids the answers but giving them chances to figure things out on their own or with their friends, and letting them ask themselves, “What do I need to figure this out? Do I need blocks? Should I draw it out?” And all of these are useful ways to navigate solving problems that even mathematicians use.
Dr. Lambert’s study on mathematicians with dyslexia revealed this feature of math, but also that students with disabilities might have strengths in perseverance. One of the mathematicians told her that his dyslexia helped him in math because it taught him how to keep going when he was stuck: “When you’re dyslexic and you’re dealing with a system that’s not designed for you, you know how to keep going, you know how to work around things. And that’s what helped me become a mathematician because that’s what you need to learn how to do. This problem is challenging, I am going to keep working, and I’m going to find a way through it.
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