This week, the State Board of Education is set to approve a nearly 1,000-page set of guidelines for math instruction, with the far-reaching and hotly debated aim of revolutionising math instruction in California, where just one-third of students—and one in five low-income students—met state standards in the most recent state standardised exam.
Whether the updated Mathematics Framework for California Public Schools will improve student engagement and accomplishment will depend on the acceptance of new textbooks and years of intensive teacher training on a scale the state has not supported in decades. There are others who doubt it, but many teachers are sure it will.
It has taken close to four years to create the updated foundation. It took 14 months to develop the third and probably final version in response to over 900 pro and con comments and petitions. A fresh group of authors affiliated with WestEd’s Region 15 Comprehensive Center—a San Francisco-based research and service organisation hired by the California Department of Education—wrote the document.
The state board only took comments until July 7 at noon after releasing the revised draft on June 26. Following a concluding hearing slated for this Wednesday, the board is anticipated to approve it, possibly with some modifications.
He declared, “The chapters on teaching and structuring school experiences for equity and engagement are the biggest and strongest part of this framework.” “The framework is supported by the maths education community and the people I regularly work with, and we are prepared to proceed and put this into practice.”
The recommendations in the framework are optional, but they strongly impact the choices made by districts, educators, and textbook publishers. The first two drafts of the framework have sparked widespread interest, partly because California, with its 5.8 million students, is the biggest and most lucrative market in the country for textbook publishers. These publishers, as the authors of the framework make clear (see Chapter 13), will need to follow its guidelines in order to be approved for the list of publishers.
However, the suggested approach also introduces a new angle to the long-running discussion about maths instruction. Math traditionalists are cautioning that most children would not succeed in the suggested student-centered, inquiry-based, “big ideas” driven instructional technique because it places less emphasis on memorising and paying attention to processes.
A planned high school curriculum that seemed to prioritise data science over the conventional calculus course sequence—which is necessary for college students majoring in science, technology, engineering, and math—was met with criticism from thousands of university STEM experts who signed petitions against it. 6,000 people signed a petition in support of the idea that districts shouldn’t begin teaching algebra in the eighth grade because the framework prevented parents of students with superior math ability from doing so. Students would have an advantage in fitting in calculus before graduating from high school thanks to the early start.
The demand for a new data science pathway was dropped by the new authors in response, and instead, they integrated data capabilities into maths instruction across grade levels. Additionally, they attempted to dispel the myth that a more demanding, math-intensive data science course, when combined with calculus, would prepare students for a data science major in college. Data literacy is a necessary course for all students in the twenty-first century.
The framework, however, ignored a related controversy that is dividing faculty at California State University and the University of California regarding whether an increasing number of UC-approved data science courses with little to no advanced math will leave students unprepared for college courses that require a lot of math.
A UC faculty senate body known as BOARS, which is in charge of approving high school course requirements, openly stated last week that it is reconsidering the authorised courses. The chair of BOARS requested in a letter dated 7 July (PDF) to the state board that references to data science courses serving as a substitute for Algebra II math requirements be removed from both the text and the diagram (see below). The letter stated that BOARS intended to investigate the matter more.
The authors of the most recent revision changed several of the works’ citations on neuroscience and other subjects, or they eliminated them entirely. A few of the work citations back up the teaching strategies advocated by math education specialists, such as Jo Boaler, a math education professor at Stanford University and one of the developers of the original framework.
At least some reviewers are still not satisfied, having hoped that a year’s effort would address all of the issues they brought up. The most vocal, if not the most prominent, of them all, Stanford math professor and head of undergraduate studies Brian Conrad, again advocated for rejecting the framework because of the flaws he listed.
Intact philosophy
The bulk of the previous year was devoted to streamlining, condensing, and rearrangement of the extensive document. The first two of the book’s six chapters, which outline how to cultivate optimistic attitudes towards arithmetic and leverage students’ varied origins as “cultural assets,” were the main emphasis of the rewrite. An appendix was added with vignettes that would be helpful for teachers to extend chapters.
Most importantly, the revised text stayed true to its main goal of making maths interesting and applicable for the large number of students who, especially after middle school, consider maths to be unapproachable and abstract. That was the direction provided by the state board, curriculum framework and evaluation criteria committee, and teacher focus groups in California.
The framework lists several classroom strategies to meet the needs of diverse students, including using “open, engaging tasks” and “inviting student questions and conjectures”; another is to “teach towards social justice,” which includes making graphs of student homelessness or analysing data on air and ground pollutants by neighbourhood.
Refusing to teach Algebra 1 in the eighth grade
Although they were not involved in the most recent revision, the previous writers largely appreciated the outcome during the webinar. Based on the chapters he had read, Brian Lindaman, co-faculty director of Chico State’s Centre for Science and Mathematics Instruction and one of the original framework’s five authors, stated that, “I have liked and appreciated the changes by and large,” including enhancements in “the readability, the flow, and the coherence of it.”
Refusing to teach Algebra 1 in the eighth grade
Although they were not involved in the most recent revision, the previous writers largely appreciated the outcome during the webinar. Based on the chapters he had read, Brian Lindaman, co-faculty director of Chico State’s Centre for Science and Mathematics Instruction and one of the original framework’s five authors, stated that, “I have liked and appreciated the changes by and large,” including enhancements in “the readability, the flow, and the coherence of it.”
Additionally, the updated framework maintained its earlier advice that almost all students should postpone taking Algebra I until the ninth grade. It does admit that “some students will be ready to accelerate” into the eighth grade and Algebra I, giving them more opportunities to enrol in advanced high school courses. However, the framework indicates that those pupils ought to be assessed for algebra preparedness and that educational institutions ought to think about providing them with summer courses similar to Bob Moses’ Algebra Project, which has been effective in preparing minority students for algebra.
Districts are in charge of determining which kids can enrol in algebra in the eighth grade. The Math Placement Act, a state law passed in 2015, mandates that districts establish objective standards for assigning children to math classes and implement those standards consistently. However, a lot of districts will accept
Eighth-grade algebra is not included as a course choice in the framework’s diagram outlining STEM and non-STEM course routes, likely in an effort to discourage broad participation in the subject. The framework uses the experience of California in the early 2000s—when the state forced districts to provide algebra in the eighth grade—to support its argument. Research revealed that many of the kids were ill-prepared and had to repeat the course without any improved results. The framework said that “success for many students was undermined.”
The more recent San Francisco Unified experiment, Conrad responds, “was a total failure, exacerbating the very inequities it aimed to prevent, and is especially misguided since this country faces a dire shortage of STEM professionals.” All children were required to master algebra in the ninth grade.
In arithmetic, a “common ninth-grade experience” is also a tactic to avoid tracking, which is the process of spotting possibly advanced math pupils in elementary school. Students who are not tracked may experience a stunting of their abilities, goals, and self-image as a result. According to Brown, these students—who are primarily low-income Black and Hispanic kids—usually have the least engaging curricula and the least experienced teachers. He asserted that tracking has legitimate negative repercussions.
“We’ve given more kids opportunities to stay on the pathway to get high-level maths classes if we can wait to hold the tracking off until at least eighth grade,” stated Cole Sampson, an administrator of professional learning and student support for the framework and a member of the education advisory group.
However, the difficulties for teachers can increase when algebra-ready kids are placed in a classroom with a diverse group of students with varying skill levels. Further, it deprives eighth graders who are prepared for algebra of a head start in high school maths. They must now take two math classes in addition to their regular math classes, sign up for a summer course, or take a difficult compression math course with extra aid if they’re lucky in order to advance to calculus. The barriers to acceleration that face low-income students with jobs may compel them to give up on their college aspirations to specialise in STEM.
A quicker route to calculus
The framework suggests that a task force look into the possibility of reducing the number of courses from four to three (Algebra I, Geometry, Algebra II, and Precalculus) in order to move from eighth-grade algebra to advanced math such as calculus by the time students reach their senior year.
Brown is sure that this is possible. Conrad expresses scepticism, pointing out that the framework drafters have three years to provide a substitute but haven’t. Katherine Stevenson, a CSU Northridge director of developmental mathematics and mathematics professor, considers herself halfway between: Reducing a course sequence won’t be feasible until the Common Core math requirements from 2013 are examined from the perspective of the standards that students will require in 2030.
The biggest challenge facing high school math teachers is creating curricula that will allow students to “exercise choice about their futures” by giving them “more opportunities to make choices that reflect their interests and aspirations.” According to the framework, school districts have a great deal of flexibility when creating third- and fourth-year curricula. Financial Algebra is one such course, which is similar in rigour to Algebra II and involves mathematical modelling related to personal
Being flexible and giving pupils options should be the main objectives. The framework includes the following student journey examples: After developing an interest in software applications, a student pursuing a non-STEM graphics arts degree decided to take Pre-calculus as a senior with a support course, preparing her for freshman calculus and programming classes. Another student who wants to work in a fabrication business after graduation takes a modelling course after completing the required first two years of math in order to grasp the mathematics involved in three-dimensional printing.
Although high school sequencing have generated the most debate, the fundamental teaching practices may have the greatest influence on the framework. The method, known to scholars as constructivism, served as the foundation for the math standards that California enacted in the early 1990s before abandoning them in 1997 in response to a popular uprising. Although they wouldn’t be novel, the adjustments might be significant enough to completely alter the way students are taught in the classroom.
The framework explains the distinction between the views on the “productive” and “unproductive” duties of educators.
The former approach, which is used in many classes, aims to “explain to students the precise definitions, formulas, and rules they should be aware of and show them how to apply this knowledge to solve mathematical problems.” The student’s job is to retain the knowledge that is taught and use it to answer common questions on assignments, examinations, and quizzes.
The goal of the latter should be “to facilitate discourse that moves students towards shared understanding of mathematics and engage students in tasks that promote reasoning and problem-solving.” Students should actively participate in making meaning of mathematical assignments by employing a variety of tactics and representations, defending their answers, drawing links to previously learned material or well-known situations, and taking other people’s arguments into consideration.
Making a connection with their surroundings
According to the framework, most students struggle with maths because there is no relationship or context between what they learn in class and what is going on in the real world. A year is broken up into units of “power standards,” each of which is taught separately, illustrated with a process, and evaluated before being moved on to the next.
An approach would be to encourage pupils’ natural interest while working towards a thorough comprehension of mathematical concepts. Math questions based on student responses should be the starting point for classes. In order to demonstrate how algebra relates to other subjects and to clusters of standards both inside the topic—such as number sense—teachers should base their lessons on “big ideas” for each grade.
According to the framework, it is imperative that the conceptual knowledge comes before the procedural stages so that we may comprehend the rationale for the actions when we eventually reach them. It’s no longer a mystery, Sampson declared.
According to Stevenson, an instructor could begin by saying, “This is the situation: What do you see and wonder about it? These are a few of the topics we will be discussing today. Which ones are familiar to you already? The steps required to solve it, such as how to multiply two digits or find a cylinder’s volume, are indicated by the answers.
“The concept of the big ideas is really important, because it prevents teachers from feeling like they’re teaching material in isolation,” agreed Vicki Murray, a learning coordinator at Buellton Unified who has experience instructing arithmetic in primary school. “Jo Boaler has done a fantastic job of illustrating the mile-high view and how this concept relates to so many other mathematical concepts.” North of Santa Barbara sits the 600-student district of Buellton.
According to Stevenson, “many K–6 teachers are really excited about it, and it makes sense to them.” As for the Next Generation Science Standards, “it’s actually asking them to teach maths the same way they teach a lot of other things.” However, high school teachers could feel confused by the methodology and overburdened by the intricate collection
“I agree that we should approach education in a different way. I acknowledge that the current course of action is ineffective. Too much is being taught too quickly, according to Stevenson. “I wonder whether what they (the authors) are attempting to say couldn’t be expressed in a more straightforward way.” She stated that pupils can leave a lesson with a “muddy sense of what they were to have learned.”
Tom Loveless, a former senior scholar at the Brookings Institution, education researcher who currently resides close to Sacramento, and author of a book on the Common Core standards, delivered a critical critique of the framework’s underlying assumptions. He claimed that the writers presented a “false dichotomy” on the necessity of “conceptual understanding.”
He expressed sympathy for the critics who claim that maths methods and facts have not been taught well. “But forcing them into the background will come at a cost.”
The prior framework made it abundantly evident that precision and speed are necessary for maths fluency. It’s problematic because the suggested framework excludes speed from ever being considered a component of fluency, he said.
In a recent article, he claimed that as students take on more complicated cognitive activities, they may easily access math knowledge that they have acquired and stored in long-term memory. The framework recommends delaying multiplication and division table fluency until the later primary grades, in violation of the Common Core criteria. He anticipates that fewer pupils will be ready for algebra in the ninth grade as a result of the continued delay.
That is what maths specialist Jane Molnar, who has worked in classrooms and as a tutor for 43 years, has experienced. Kids simply can’t keep up if they don’t grasp certain concepts in the first, second, or third grades and are just exploring and discussing numbers. And if this pattern persisted until middle school, children who were unable to divide using the division technique would find it extremely difficult to divide polynomials in algebra.
Instruction is necessary.
Proponents of the framework concur that teachers who lack substantial subject-matter expertise will require extensive training.
“Those who really have a very regimented routine about how maths should be taught are going to be uncomfortable at first,” Sampson added.
The framework “will really influence the way that teachers think about teaching and engaging their students,” according to Brown, who expressed this as his greatest aim. “The state will not really fully fund the rollout and provide teachers with the support they need to really implement it,” is his greatest concern.
The initial authors of the framework, like Brown, predicted enormous rewards.
According to Boaler, “one of the goals of this framework is to dispel the myth that only a select group of students can perform at a high level in mathematics and to make this wonderful subject accessible to everyone.”
“If my students start arriving at university understanding mathematics as a set of lenses for exploring questions that they’re actually interested in, I would be ecstatic,” Sonoma State University math professor Ben Ford stated. And that’s one of this framework’s objectives.
But Loveless thinks history will repeat itself.
