Big changes are coming to how schools teach math in California, shifts in instructional practice that could have ripple effects across the country.
But that process may take a while.
Last week, the California State Board of Education approved the new California Math Framework, a guiding document for curriculum and instruction in the subject that has been the object of intense controversy over the course of its 4-year development.
The framework outlines a new vision for math teaching, emphasizing inquiry-based instruction, real-world problem-solving, and data science and data literacy. It also suggests that districts鈥� math course sequence put 9th graders in Algebra, rather than tracking some students into it in middle school.
While these recommendations aren鈥檛 binding, they will dictate the content of approved curricula and the direction of professional learning. These shifts could have national implications鈥擟alifornia is one of the biggest education markets in the country, and as such has a large influence on the curriculum landscape.
Even so, many of those changes are still years down the road.
The process of turning guidance into changes in classroom practice is long and complicated, requiring collaboration from many different actors, including the state department of education, districts, outside technical assistance organizations, and publishers.
鈥淭here are all of these different levels that work together to make sure that the implementation is successful,鈥� said Maryia Krivoruchko, a director at UnboundEd, an organization that provides professional learning and support for schools.
Here are some answers to questions about what might happen next.
What is a framework, and how does it shape instruction?
California鈥檚 curriculum frameworks offer guidance for how to implement the state鈥檚 instructional standards in different subjects. Think about a road trip: If standards are the destination鈥攖he end goal of what the state wants students to know and to be able to do鈥攁 framework is like driving directions. It offers suggestions for how to get students where they need to go.
But neither is the framework a curriculum鈥攖he daily activities, materials, and steps that teachers use to build knowledge towards mastery of each standard. (While it offers examples of what teaching might look like in 鈥渧ignettes,鈥� the framework doesn鈥檛 provide a comprehensive set of lessons or activities.)
The math framework lays out recommendations for how students should progress in the subject throughout the grades. One of the framework鈥檚 biggest controversies arose out of its draft recommendation that many students take Algebra in 9th grade.
The final version of the framework that the state board adopted suggests that schools offer Algebra in 9th grade, but also notes that 鈥渟ome students鈥� will be ready for the subject earlier. (For more on this topic, see this story.)
The document also offers guidance for planning instruction. It tells teachers how to organize different topics and standards into what the framework calls 鈥渂ig ideas,鈥� and how to connect these big ideas throughout the grade and between grades. And it suggests that teachers focus on inquiry-based learning and classroom practices that can help foster equity.
While it isn鈥檛 a curriculum, it does provide recommendations for what curricula should look like鈥攃riteria that publishers will need to meet in order to make it onto the state鈥檚 list of approved materials.
How does the framework suggest teaching should change?
The document says that teaching should be organized around 鈥渂ig ideas鈥� that connect math concepts, rather than focusing on discrete standards one-by-one. 鈥淏ig ideas and the connections among them serve as a schema鈥攁 map of the intellectual territory鈥攖hat supports conceptual understanding,鈥� the document reads.
Schools will still teach the standards. A 2nd grader, for example, will still learn how to solve word problems that require adding and subtracting within 100. But that standard is now under the big idea of 鈥渘umber strategies,鈥� a category that includes conceptually related skills鈥攍ike using different strategies for 2-digit subtraction and understanding the meaning of place value.
To teach in this interconnected way, the framework suggests teachers center 鈥渟tudent investigations of intriguing, authentic problems.鈥� Here鈥檚 an example of what that might look like in a middle school class targeting standards around proportionality and fractions:
One middle school teacher, for example, presented her students with the dilemma of a swimmer being followed by a baby whale. Should the swimmer guide the baby whale out to an oil rig where the baby鈥檚 mother has been seen鈥攁 risk to the swimmer鈥攐r head safely to shore, which is safer for the swimmer but risks [the] baby whale getting beached?
Enchanted by the story, students spent time on math-related tasks such as synthesizing information from different sources (maps, cold water survival charts), learning academic vocabulary to decide which function they may apply, and organizing data into number lines, function tables and coordinate planes鈥攌ey aspects of this teacher鈥檚 curriculum. They analyzed proportional relationships, added fractions, compared functions, and used data. In short, they learned math content, explored content connections, and employed mathematical practices as they persevered to solve an interesting, complex problem.
Will teachers have to create these investigations themselves? Where will they come from?
The framework is likely to prompt a shift in the curriculum market in California.
In addition to guidance on instruction, the document also provides criteria for evaluating K-8 curriculum materials in math. Publishers need to meet these criteria to make it onto the state鈥檚 approved list. California doesn鈥檛 require districts to select those materials, but the recommendations hold sway.
The new criteria reflect the framework鈥檚 emphasis on inquiry-based instruction. They say that students should 鈥渟pend the large majority of their time on mathematical investigations that address the big ideas of that grade.鈥� Activities are supposed to help kids 鈥渞eason mathematically in age-appropriate contexts.鈥�
Materials also need to offer guidance for differentiation, including for English learners and students with learning disabilities.
The framework notes that new curricula will be approved in a 2025 adoption, but there鈥檚 no official timeline yet. The board will likely propose a schedule of events at a future meeting, said Mike Torres, the director of the Curriculum Frameworks and Instructional Resources Division at the California Department of Education, in a statement.
The state鈥檚 education department is planning rollout activities, including professional development, he said.
For a sense of how long this can take, consider that California adopted a new science framework in November of 2016, but did not approve matching science materials until two years later, in 2018.
How long will it be before these changes affect classroom practice?
That鈥檚 going to vary widely. Individual districts have a lot of autonomy over the materials that they use and the instructional approaches they champion.
鈥淪ome may already be teaching in a very similar manner that鈥檚 described in the framework, and for some it may be a big shift,鈥� said Krivoruchko.
Survey results from a show that California math teachers are already slightly more likely than math teachers in other states to say they place a high priority on conceptual understanding.
Still, the shifts that the framework proposes are significant, and go beyond mere emphasis on conceptual understanding. They also change the underlying structure of lessons. Instead of being oriented around mastering individual standards, teaching is supposed to be oriented around investigations and questions that students explore through the standards.
This format鈥攖eaching students skills, formulas, and foundational knowledge through an investigation鈥攊s akin to methods laid out in the Next Generation Science Standards.
When these standards were released in 2014, they proposed similarly sweeping changes to science instruction. Twenty states and the District of Columbia have adopted them, and 24 states have developed their own standards based on this framework. Even so, shifting instructional practice to align to these standards, and finding suitable materials, is still an ongoing challenge for many teachers almost a decade on.
Many California districts will probably wait for the state鈥檚 list to adopt new materials, but others may undertake the process sooner, on their own鈥攁n option that the state permits.
And even when districts do bring in new curriculum, there are likely to be wide variations in how much these materials influence teachers鈥� practice.
The WestEd report found that only 38 percent of California math teachers said that their district leaders made the decision about which materials they used in their classrooms鈥攕uggesting, the authors wrote, that the teachers had a 鈥渉igh level of autonomy in their work.鈥�
