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All of us should be heartened by the just-released revision of the new California Framework for Mathematics.

While the earlier drafts of the framework prompted concerns that the effort to achieve greater equity would hold high-achieving students back from excellence, this revised draft makes clear that will not be the case.

The goal is to increase the number, diversity and preparedness of high achievers aspiring to specialize in science, technology, engineering or math, or STEM, fields while all California students become more mathematically engaged and accomplished.

The framework, which will guide how the subject is taught in California’s K-12 schools, builds on the 2013 framework which looked inward to the mathematics. The 2022 framework faces outward to the students. We can move forward instead of back and forth.

Mathematics belongs to everyone. The framework has placed a major emphasis on improving how school mathematics responds to differences among students. I think this is justified by the system’s history of weakness and failure in responding to this challenge.

While there have been important improvements in instructional materials, the status quo does not work very well for many — or even most — students. This has been true for a long time. Ask almost any parent or student.

Take a look at performance data: California ranks in the bottom third of states on the National Assessment of Educational Progress in mathematics, and the U.S. ranks far below the average on international assessments like PISA.

To change this, we must tackle some critical challenges thoughtfully with a problem-solving approach. Some issues the framework addresses that are most important include:

**Schools must do a better job in elementary school of teaching everyone what’s most important for succeeding in middle and high school mathematics.**As the framework emphasizes, this will require learning conditions that recognize and respect each student’s thinking as the work of learning and develops each student’s belief in themselves as learners.**The basic human conditions for learning should not depend on a student’s background, ethnicity or gender.**Every student deserves the opportunity to be listened to while learning mathematics, to be recognized as a problem solver and thinker. The status quo fails too many students, treating them in ways that demoralize them, discouraging rather than encouraging effort. The math-anxious, math-cynical students are then delivered to middle schools. This must stop.**Schools should put each student in the best position to achieve their aspirations.**Students with aspirations for STEM careers should have the opportunity to excel in mathematics, taking well-taught coursework that allows them to reach calculus with a deeper understanding. Students with aspirations in law, business, the arts and humanities, nursing, careers as first-responders and media should have the opportunity to learn exciting and engaging mathematics useful for their futures. The framework outlines course options that can enable all students to reach their aspirations.**Schools should prepare students aspiring for careers in STEM for further work in mathematics relevant to their fields.**Earlier versions of the framework did not say enough about this. The new version does. This version takes advice from university faculty regarding what is important for entering STEM majors. Yes, it includes being prepared for serious work in calculus. Although some students find their way through the status quo to success in STEM, we need to modernize STEM preparation in ways indicated by the revised framework.**Colleges should be able to recruit and prepare STEM aspirants from a larger pool than we have done, historically.**This includes doing a much better job of supporting Black, Latino, Native American, Pacific Islander and female students to engage in, enjoy and succeed in mathematics that prepares them for STEM. We need to expand the methods used to find, assess, and develop STEM students.**Schools and colleges should keep students’ options to prepare for STEM fields open as long as possible.**Given the gaps in opportunity that correlate too strongly with poverty, race and gender, schools must avoid early tracking systems. Acceleration should be an option for students at the end of middle school and again in high school. Opportunities to pursue advanced mathematics should not be lost because of placement in middle school. This requires work from everyone. It*does not*require lowering standards. It*does*require humanizing the conditions of learning: developing students’ beliefs in themselves as learners and building on the different assets students bring.**Schools should prepare students aspiring to fields where mathematics and statistics are important from a user’s perspective.**People working in fields such as economics, medicine, and the social sciences need courses that focus on deeper, more robust experiences*using*mathematics in varied situations in ways that take advantage of calculators and computers. While such courses would be valuable for STEM students in addition to advancing toward calculus, they are critical for students with other aspirations. We especially need to modernize this kind of understanding of data science and computation in the curriculum. The revised framework develops useful and important ways to make improvements in programs for students through more modern approaches to data science.

The framework provides guidance to help teachers find and spend more time teaching the most important concepts in the curriculum, tackles the “math is boring” problem facing most students by illustrating engaging pedagogies and assignments, and emphasizes the importance of supporting high achievers as well as students who struggle along the way.

The framework also builds on research on learning, motivation and what high-achieving countries do in teaching mathematics. This includes students articulating their reasoning, explaining their problem-solving approach and learning to make connections across mathematical topics and between mathematics and its applications in the world around them. It also addresses the need for students to identify themselves as effective learners of mathematics and develop a sense that they belong to the community of mathematics learners. Above all, it provides guidance on how to develop students’ beliefs that they can get better at mathematics by putting in the work to learn.

The work of making things better is work. It is not enough to take stands; it is more important, now, to take steps.

The California framework could have, as often happens, shrunk away from the tough issues. It did not. Thank you.

Let’s take this framework and get to work.

•••

**Phil Daro** was a lead author on the Common Core mathematics standards and consults with school districts, states and higher education institutions to improve the teaching of mathematics.

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## Comments (5)

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Dawn5 months ago5 months agoThis new “framework” is all about politics. It is a travesty to the education of our children to again bring race into everything. Math is taught equally to all, there is no bias in numbers. Start educating instead of indoctrinating.

Wujing Harrison7 months ago7 months agoWhat if everyone already used some forms of calculus thinking? Even if they may have not learned it officially. I am yet to meet someone who doesn't apply calculus logic in life. For example, if you get one sticker per day, you get 7 per week. If you get two per day, you get 14 per week. Incremental changes have an accumulative effect. Calculus can be introduced in its preliminary form in elementary curriculum. The … Read More

What if everyone already used some forms of calculus thinking? Even if they may have not learned it officially.

I am yet to meet someone who doesn’t apply calculus logic in life. For example, if you get one sticker per day, you get 7 per week. If you get two per day, you get 14 per week. Incremental changes have an accumulative effect. Calculus can be introduced in its preliminary form in elementary curriculum.

The problem with math education is that students are not taught explicitly the principles of counting, hence addition and subtraction, the rate of change, hence multiplication and division. They cannot think with math.

The concept behind counting is the categories. Can you continue to count, with an apple and an orange? Yes, but in a different category to include both fruits. How about a rose? A frog? A rock? Yes. A day? A light year?

What are the concepts or principles of multiplication and division? Say 2+2×2. Most students cannot articulate the difference from categorical perspective, hence cannot explain why of the orders of operations. They may gain technical proficiency, many cannot understand the logic nor appreciate it, since they are not taught about it.

Equity is achieved when students can understand mathematical logics. Those are need to be in the framework.

M DeYoung8 months ago8 months agoRemove word “equity” and replace with”excellence!” Politics had no place in real education.

Jim8 months ago8 months ago“U.S. ranks far below the average on international assessments like PISA.” Then why not teach the same way other countries do?

Replies

Ava8 months ago8 months agoJim, I think it is because the teachers and the school boards will need to train and educate the teachers to learn how to do their job more effectively and efficiently. Also, schools should keep the students to repeat the level if the student didn't do well, like other countries do. But it is all about the money spent and keep pushing the students who are already failing to fail more and then to prepare … Read More

Jim, I think it is because the teachers and the school boards will need to train and educate the teachers to learn how to do their job more effectively and efficiently. Also, schools should keep the students to repeat the level if the student didn’t do well, like other countries do. But it is all about the money spent and keep pushing the students who are already failing to fail more and then to prepare more programs to help them to fail to justify the reason of their failing. We personally have been dealing with one bad teacher this year at the elementary school level. Any idea if we can do anything and how to eliminate bad teachers from educational system?