Many California parents with kids transitioning to high school face the algebra dilemma. Your child may be working toward a diploma on a traditional high school diploma track, or they may be on the alternative pathway to a diploma for students with a significant cognitive disability. Either way, you have likely been told that they have to pass Algebra I.
But is algebra really useful for kids with disabilities, beyond just earning that diploma? And how do we work with our teachers and IEP teams to make algebra inclusive and accessible for our kids? We’ll explore how algebra can be meaningful, even for students pursuing the alternative pathway, who have significant cognitive disabilities that require modifications to their work. But first, we review the requirement to pass Algebra I. Later, we’ll also discuss the supports available to help students who aren't eligible for the alternative pathway succeed in this challenging class.
To find out, 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. We asked both our experts what benefits a student with extensive support needs might get out of studying algebra.
Algebra is a branch of mathematics that uses mathematical statements to describe relationships between things that vary. It uses these equations to solve problems using mathematical reasoning. Students begin to use algebraic strategies in elementary school. By the time they reach high school, they’re expected to use those skills to tackle more complex problems and think critically in a mathematical way. It’s a key step in building reasoning skills they’ll use for years to come.
Algebra 1 and Mathematics I classes in California high schools cover content standards in concept areas Number & Quality, Algebra, Functions and Statistics & probability. For example, students are expected to learn “how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. For example, we define 51/3 to be the cube root of 5 because we want (51/3)3 = 5(1/3)3 to hold, so (51/3)3 must equal 5.”
For many of us, that seems too abstract for students with a cognitive disability to master, and not particularly useful. Parents often have forgotten much of what they learned in algebra because they have not used radicals or rational exponents in everyday life. In the traditional way that algebra has been taught, there is little attempt to connect these tools to solving everyday problems. But algebra can actually be meaningful for kids with disabilities, our experts tell us. More on this later in the article.
The state requirement for a diploma includes two years of high school math, of which one must be Algebra I or Mathematics I, or must have the rigor of Algebra I. Note that where districts have a two-year Algebra I class, that could qualify.
Most districts have tougher local requirements for a diploma, usually including Algebra 1 & 2 and Geometry, or Mathematics I-III. In addition to students on the alternative pathway, kids with parents in the military and kids who are served by the foster system may sometimes be allowed to qualify for a diploma using the state requirements.
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.”
What about A through G standards?
In recent years, school districts have also been aligning their local requirements for a diploma with the University of California A through G standards, which are courses needed to meet the minimum admission criteria set by schools in the University of California and California State University systems. That effectively means that not only is Algebra I/Mathematics I required, but also in many cases, Algebra II/Mathematics II & III. The UC requirements for math classes are set out here. Note that for entrance to a UC, a grade C or above may be required. Schools may accept a grade D for graduation.
For example, in line with CSU/UC requirements, Los Angeles Unified School District requires three years of math. Long Beach Unified School District, on the other hand, requires 40 credits of math. Within those 40 credits, students must successfully complete the equivalent of Algebra I and II. San Francisco Unified School District requires three years of approved UC math, typically Algebra I, Geometry, and Algebra II.
According to Disability Rights California, yes, but there are options. “Students with disabilities, who have attempted but did not pass Algebra I, even with necessary and appropriate support services and accommodations, should consider asking their school district to request a waiver of this requirement from the State Board of Education for purposes of receiving a diploma. [Cal. Educ. Code Sec. 56101.] Waivers are not always granted, but the waiver process is the only way for a student with a disability, who cannot pass the Algebra I, or any other course or graduation requirement, to still receive a diploma.” Students on the alternative pathway to a diploma are not excluded from this option.
Students on a traditional diploma track: these students are able to use alternative means of accessing the curriculum, and alternative means of showing their learning in an algebra class. These might be part of a universally designed class or written into their IEP as accommodations. The new CDE website Coursework for a Diploma provides teachers with lots of ideas for accessible math instruction that maintains the rigor of the state standards. This includes teaching guides that contain suggestions for alternative means of expression, such as using assistive technology to write equations or draw graphs.
Students earning a certificate of completion: these students are not required to take Algebra I. Many take functional math or essential math classes. These classes focus on basic skills, such as telling time and using money. There is often little or no defined curriculum other than each student’s individual IEP goals, and teaching is rarely evidence-based. In light of the alternate pathway to a diploma, many of these classrooms have been adopting a new curriculum that is ‘aligned’ with the state standards, but still focuses on functional skills, such as the use of time and money. If you’re still unsure, check in with your school and child’s teacher to make sure their special education math curriculum is aligned with state standards.
Students on the alternative pathway to a diploma: note that using modifications (changes to the achievement standard) in Algebra I might disqualify a student from earning a diploma unless the student is eligible for the alternative pathway. In this case, students with significant cognitive disabilities will be held to the alternate achievement standards.
That said, some high schools provide a four-year or two-year algebra class that fulfills both the requirement to pass algebra and the requirement for two years of math. To find a list of classes that your specific high school offers, search here. Many schools are now adding new math classes aligned with grade-level state standards to work with both the new alternative pathway to a diploma and the new California Math Framework.
Let’s dive deeper into students taking the alternative pathway to a diploma. For these students who aren’t able to meet the regular CCSS in math, special education math teachers can provide specially designed instruction to focus on the Essential Understandings (EU) (in both an inclusive class or in a separate setting) instead. These EUs are aligned with the CCSS standards that all students learn but they were created for students who are using Alternate Assessments and need a modified general education curriculum.
So, if you have a student who is using alternate assessments and on the alternate pathway to a diploma, they can pass Algebra I using alternative achievement standards based on the Essential Understandings. (Note that some students will also be able to work towards the math Core Content Connectors, which pick out and break down the most important skills from the CCSS so that children who need more support can learn the same content as their peers.)
The algebra problem: your child is working on a real-world problem — figuring out how many apples they can buy with $10. Here is an illustration of how a student who is still working on limited math skills might achieve that (after a great deal of practice).
The algebra problem: your child is working on a real-world measurement problem — figuring out how many cups of flour they need to make 36 cupcakes for the class. Here is an illustration of how a student who is still working on limited math skills might achieve that.
Here is an illustration of how a student who is still working on limited math skills might achieve that using the Essential Understanding.
For some high schoolers with significant cognitive disabilities, this problem might be too simple. If a student is further along, the teacher can challenge them using the Prioritized Core Content Connector instead of the Essential Understanding we mentioned earlier. For example, the student may have been working on understanding that 22 is like the area of a square and 23 is the volume of a cube. But multiplying a square and a cube is tricky to present visually or concretely. The student can still use visuals to complete the math problem, as in this example.
Algebra is also useful because students learn to use charts and tables. For example:
The algebra problem: your child is working on a real-world problem — figuring out how many friends Sam has using numbers of candy. Here is an illustration of how a student on the alternative pathway to a diploma might solve this using the Essential Understanding — they could arrange six counters into three sets of two, or two sets of three.
A more advanced student might work on the Core Content Connector instead, as shown here.
Now that you've started to explore EUs, we hope you can see how Algebra can be designed for a diverse set of learners. Now let's learn why it can actually be meaningful. For parents of kids with cognitive disabilities, there may be a shift away from the traditional curriculum toward a focus instead on practical math skills that better align with their child’s needs. Our experts said that algebra can actually be meaningful for kids with disabilities, including those with significant cognitive disabilities.
Noland argues that algebra is a means to make sense of our world, such as figuring out patterns, understanding data presented on a graph, recognizing the connections, and determining solution pathways. Listen to her explanation here:
Dr. Lambert explains that algebra can be meaningful: “It can be visual, it can be fun, it can be engaging, and there’s real value there for kids. It just needs to be taught in a way that really makes sense to children,” she explains. While some kids with disabilities thrive on the more verbal, abstract teaching of math, that doesn’t work for all kids. For others, algebra is better understood when it moves toward more visual and concrete learning.
In an inclusive classroom, kids may be working on puzzles, using blocks, and generating conversations that are about the generalization of a variable. The VisualPatterns.org website is a great example of how visual sequences can be engaging for people of all abilities. Kids work out how the patterns are growing, and they use that to start generalizing mathematics.
Dr. Lambert adds, “Including a student with intellectual differences in a general education math class would probably be wonderful for everyone if the teacher took it quite seriously and made sure that everything was concrete, everything was real, they understood the concept of a variable and equivalence, and it was so visual and real to kids that it made a ton of sense. That would be amazing because the inclusion of that child would make it better for all those other kids who are getting bored out of their minds when algebra becomes totally decontextualized.”
For many parents, it is impossible to imagine that a student who is still working on basic addition would benefit from studying algebra. Dr. Lambert’s approach is to design instruction that begins with number sense, but it’s also centered on a core idea in algebra.
For Dr. Lambert, “This is about IEP goals, but this is also about inclusion in mathematics. It requires a lot of understanding of mathematics to do this work because you need to be able to say, ‘Okay, algebra: what is the core idea here I want this child to come out with?’ They’re not going to understand everything about algebra in the seventh grade class, but what is core and important? it might be equivalence; it might be matching graphs with equations. You have to pick something that really matters, that’s ambitious, and that’s high-leverage. But that requires mathematical understanding. And so sometimes that can be pretty tricky for parents and teachers, which is why I continue to advocate for more professional development for special educators.”
Noland explains that for kids with more complex needs, it’s important to look at what routines we’re building for the student to engage in algebraic concepts with their peers. Their IEP goals and objectives need to be related to problem-solving. We can also tie IEP goals to the Standards of Mathematical Practice (SMPs) that are the same for all grade levels. These standards teach students how mathematicians solve problems, for example focusing on modeling and using mathematical language. See our articles on Making Math Work For Kids with Disabilities and Math Goals in the IEP for more information.
As Noland tells us, “I do agree algebra is scary, it’s very complex. But for every student, I think we can find the purpose and the goal for them. And I think algebra can be very exciting. It’s very visual. The opportunity for communication is just really great. So I think there’s a lot of opportunities for learning.”
For more help with algebra, and math in general, head over to our article Math Curriculum Materials, Tech, Apps, and More!
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