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The State of Connecticut is opening the door for local districts to rethink the way they teach mathematics, including alternatives to ability-based “tracks” and opportunities to broaden the variety of courses that will meet graduation requirements, in part in response to stubbornly low student achievement.
Last month, the State Board of Education adopted a Joint Position Statement on Equity in Mathematics Education that underscored the need to give every student the opportunity to succeed in mathematics, and to modernize courses to include “21st century content and skills.” The statement was written in collaboration with three organizations representing the state’s mathematics teachers.
“The mathematical needs of work and life have changed immeasurably over the past decades, especially with the arrival of technologies, yet current PreK-12 mathematics remains rooted in past practices and content,” the statement reads. “The emphasis continues to be paper-and-pencil algorithmic skills at the elementary level and programming that prioritizes a pathway to calculus at the secondary level.”
Part of the impetus for changing how mathematics is taught is the poor performance of students in mathematics. Last year, only about a third of 11th graders who took the SAT in Connecticut met the minimum state standard for mathematics. And the gaps in performance fell starkly along racial lines. While nearly half of White students who took the SATs met state standards, only 10 percent of Black students and 13 percent of Hispanic students met the state standard.
A new curriculum
Jennifer Michalek, a math consultant for the State Department of Education and an author of the equity statement, told CT Examiner in an interview that one area of mathematics the state has neglected is the teaching of data analysis, including statistics and probability.
“For too many of our students, that is not done at a foundational level until late in high school, where some students never have that. And in a data-determined society, I would say that would probably be one area of need,” she said.
Middletown, which is an early adopter of the approach, approved the addition of a data science course last year.
Jillian Cavanna, an assistant professor at the University of Hartford and the president of the Associated Mathematics Teacher Educators in Connecticut, or AMTEC, told CT Examiner that the advent of new technologies meant that there was less need to teach rote computation, which can be accomplished with calculators and computers, and more need to teach critical thinking and reasoning skills.
“The idea is, we can compress some of these things that computers do better and faster than we do, and that gives us lots of space,” said Cavanna. “It’s not that everyone just finishes math early now, but instead we can have more space for things like statistics and modeling with mathematics – so, mathematicizing real life problems — thinking about data science, things like reasoning and problem solving or tackling problems that students don’t already know how to do.”
Cavanna said that the speed at which technology develops means that educators need to give students the skills to solve problems that people haven’t even thought of yet.
“As technology advances, we are not going to know what the questions are that students are answering,” said Cavanna.
That approach to computation did raise some concerns for Alan Taylor, a member of the State Board of Education, who commented on an earlier version of the draft statement to say that even though students had calculators to solve math equations, they needed to be able to look at a solution and know whether or not it made sense.
“I fully agree that mathematical reasoning and problem-solving are the skills we seek to develop, but I worry about leaving kids at the mercy of their machines (and their thumbs) if they don’t have at least a strong intuitive sense of what the answers their machines should be generating are,” Taylor wrote. “Deep mathematical reasoning that generates the wrong mathematical answers isn’t sufficient … While I agree that no student should be held back because of an inability to compute, I think that should mean that it is our obligation to be certain that all students can compute.”
Taylor told CT Examiner in an email that he understood the authors “would make changes that addressed my concerns.”
Cavanna said that by eliminating, at the state level, the requirement for high schoolers to pass Algebra II before graduating, there would be more opportunity for math instruction that took advantage of alternate pathways.
Megan Staples, an associate professor at UConn’s Neag School of Education and the past president of AMTEC, said that a 21st-century approach to mathematics is one that emphasizes critical thinking and prepares students for the job world, while also allowing them to make decisions about critical issues in society.
“Collectively, we are a democratic society and we need to be having collective decision making — and that should be math-informed decision making,” said Staples. “So if somebody is weighing in or voting on a bond proposal, a new library, some environmental issue, all of those things require strong mathematical thinking, and we need to be sure that all students are being prepared to manage all the mathematical demands of their lives.”
The California controversy
The drive for an updated and inclusive curriculum in mathematics has devolved into a multi-year battle in California, where the new California Math Framework originally advised against having students take Algebra in 8th grade and offered courses like data science and statistics as alternatives to calculus. A revised version of the framework, approved in July, walked back some of the updated guidelines.
Connecticut’s Joint Position Statement cites the work of Dr. Jo Boaler of Stanford University, one of the authors of the California Framework, who has advocated for the teaching of data science as an option in lieu of Algebra II and for restructuring the calculus pathway so that it would not require students to begin a calculus track before reaching high school.
Critics say that her work will actually harm Black and Brown students by pushing them into the “lower track” of data science rather than encouraging them toward calculus.
But in Connecticut, proponents of the approach say they aren’t advocating for a specific curriculum or for changes to courses already offered by local schools, instead they say, the Joint Position Statement is an opportunity for local school districts to reconsider how math is taught, and they could create an environment where all students are able to succeed at math.
Connecticut’s position statement cites a paper written by the National Council of Teachers of Mathematics emphasizing that math should be not only about career or college prep, but also about the ability to use math skills to make personal decisions, to decide whether political or scientific claims can be trusted and to appreciate the “beauty and usefulness” of the subject.
“We realized that, in many districts, all students aren’t necessarily able to access the same levels of mathematics that other students had the ability to do. And when I say levels of mathematics, that doesn’t always just mean calculus. That could mean statistics, data science — other areas of mathematics that would be just as meaningful for them when they leave high school,” said Jeffrey Corbishley, the past-president of the Associated Teachers of Mathematics in New England.
Avoiding “dead end” classes
Proponents of the changes also emphasized that the mathematics curriculum should be engaging and relevant to students from all different backgrounds.
“I don’t think it would be controversial to say engagement is a huge issue in middle and high school right now,” said Staples. “So we need to make changes to either the ways we’re instructing and or what we’re offering in order to engage students. And that has to do with looking at – What are their needs? Where are they coming from? Where are they going?”
And proponents of the changes emphasized a needed shift from emphasizing student weaknesses – what they call a “deficit mindset” – to their strengths.
The Joint Statement criticized an approach, perpetuated through “tracking,” that assigns students to higher and lower-level courses based on their abilities and relegates many students to remedial classes where less is expected.
“In the past, there were a lot of dead-end classes available to kids, done through remediation,” said Christie Madancy, president of the Connecticut Council of Leaders of Mathematics. “And so we’re learning how to better meet the needs of students and still provide a solid mathematics education.”
Staples said remedial courses are more likely to be taught by less qualified teachers and substitute teachers.
Michalek reasons that dividing up students based on ability can keep students from reaching higher levels of mathematics. She cites the practice of teaching Algebra I in 8th grade to some students but not others, which she said can prevent later-blooming students from taking calculus in high school.
“As students move up in the grades, if we track too early, we may be making determinations about students’ outcomes — that they have no other choice but to stay on that path,” she said.
At the local level
At least a handful of Connecticut schools have already adopted, or are considering, changes to the curriculum.
Madancy, who is the math coordinator at Wallingford Public Schools, said the district already offered a variety of high school mathematics courses, including a traditional calculus pathway, a data science course, and a course through Goodwin University for engineering and mathematics. She said the district was piloting a geometry course tailored specifically for students planning to find jobs in the construction industry.
Madancy said the district has also debated eliminating some of the different levels of courses offered. In Wallingford, for example, there are currently four levels of math instruction, from Advanced Placement to General.
Corbishley, who is also the grade 6-12 math supervisor at Ridgefield Public Schools, said Ridgefield had completed a year-long study of courses in mathematics at the middle and high school levels. In the end, the district decided to retain the traditional three-year sequence of Algebra I, Geometry and Algebra II, but he said the district hadn’t yet decided what advanced courses they planned to offer.
Corbishley said the district wanted to ensure that students were taking math courses that would be relevant to their futures — not only potential engineering or physics majors, but potential biology, psychology or economics majors.
In some cases, the changes in Connecticut have been met with parent opposition. Recently in Middletown, for example, parents attending a Board of Education spoke against the district’s move toward “integrated” Algebra and Geometry courses, which would combine Algebra I, Geometry and Algebra II into two years.
Daniel Long, a research scientist at UConn’s Neag School of Education, said the better solution would be to bring back Pre-algebra for 7th graders and work toward a goal of getting more 8th graders to take Algebra I. He also cited a 2023 working paper by Brown University that found negative outcomes from San Francisco’s decision to have all students take Algebra I in 9th grade.
“We believe that students with sufficient early support, high expectations and a challenging curriculum can learn advanced math regardless of race, ethnicity, or economic agenda,” Long told the Middletown Board of Education.
College acceptance
A further concern cited by some critics of the proposed change is ensuring that colleges accept the new varieties of classes.
But Cavanna said the majority of colleges don’t require Algebra II, and the few that do are open to reconsidering it.
“When we brought that to the attention of one of the colleges that did, there wasn’t a real reason,” said Cavanna. “It was simply history. It was something that somebody had decided a long time ago. And they were willing to reconsider – what does this provide?”
Corbishley said that local boards of education will be responsible for making the majority of the decisions about an updated curriculum, and they will have to make sure those decisions are tailored to the needs of their students.
“Local Boards of Eds … need to take a really hard look at their student population. They need to look at where their students are going post K-12,” said Corbishley. “Every district is different. Every group of students in the district is different. You just have to do what’s best for the students within your district.”