Insights & Impact
Extending Mathematical Practice Standards Across the Curriculum
One of the earliest promises of the Common Core State Standards Initiative was the possibility of greater integration of concepts and skills across subject areas. While many teachers embraced this idea, others were overwhelmed simply getting to know the new standards within one subject, much less trying to integrate across subject areas. But, as teachers have gotten to know the standards better, many have begun to seek out the connections that the new standards offer.
One approach that has recently started to gain traction is to extend the Common Core Standards for Mathematical Practice across the curriculum, treating the practice standards as cross-curricular thinking skills. To encourage this line of thinking, I have put together a description of the ways in which each of the Mathematical Practice Standards could apply to other subject areas. My hope is that the following ideas get your creative juices flowing and that you are inspired to expand upon them in your classroom or with your colleagues.
1. Make sense of problems and persevere in solving them. In any subject matter, students can realize that becoming proficient with any new skill requires a productive struggle to overcome hurdles and solve problems. Students learn to become patient problem solvers who can explain the meaning of a problem or task and look for ways to solve or complete it, even when a solution or path forward is not immediately apparent. They can learn to try multiple approaches and take time to devise a plan to solve a problem, complete a task, express their feelings, present a logical argument, or create a work of art.
2. Reason abstractly and quantitatively. In mathematics, students learn the ability to decontextualize and the ability to contextualize. These same abilities can apply across all subject areas as students learn the value of using metaphors or analogies to make abstract concepts concrete or to generalize from specific examples. Likewise, while students are able to think in concrete terms about objects or events that are available to the senses or that can be quantified or counted, they also learn to think in abstract terms about concepts or ideas, such as place value, infinity, friendship, love, death, and prejudice, to name a few.
3. Construct viable arguments and critique the reasoning of others. One of the most common associations that teachers have made with Common Core is the need for students to refine their skills in constructing arguments using evidence. Across subject areas, all students — including English learner students — hone their questioning and academic language skills as they participate in discussions involving questions like “How did you figure that out?”, “How did you come to that conclusion?”, “Explain your thinking,” and “What evidence supports that?” They not only explain their own thinking but also learn to listen to others’ explanations and decide if the explanations make sense.
4. Model with mathematics — and in other subjects. In all curricular areas, students can form the habit of representing problems, situations, hypotheses, or arguments in multiple ways that include using words, creating visuals, using objects, using graphic organizers, acting out, making a chart or list, creating equations, and so on. Students can also be given opportunities to connect and relate those different representations to each other and to explain their reasoning behind the connections that they have identified. They can also learn to evaluate the utility of different representations and determine which are most useful in any given situation.
5. Use appropriate tools strategically. When reading, writing, performing a task, conducting an experiment or investigation, building, drawing, sculpting, or solving a problem, students should consider the available tools and decide which tools might be most helpful. Students know that some tools are physical objects, such as rulers, thermometers, dictionaries, atlases, etc., while other tools are strategies or procedures such as “counting on,” close reading, brainstorming, goal setting, collaborating, etc. Students know when technological tools, such as Internet searches, grammar checkers, spreadsheets, or calculators might be appropriate, and they know how to use those tools to explore and deepen their understanding of concepts.
6. Attend to precision. Students refine their communication skills by learning to use clear and precise language in their discussions with others and in their own reasoning. Students use appropriate vocabulary when referring to specific content or concepts. They pay attention to details when solving problems and when formulating opinions or arguments. They are careful when following procedures, and in mathematics and science they specify units of measure and calculate accurately and efficiently. In all subject areas they learn to examine claims and arguments for accuracy.
7. Look for and make use of structure. In mathematics, students learn to discern patterns or structures in numbers, shapes, or equations. But, they can also be encouraged to see patterns and structures in other subject areas. For example, in language arts they learn to see patterns in the way that words are spelled and pronounced; they see patterns and structures in the way that root words, suffixes, and prefixes are put together to form new words; students see that texts have deliberate organizational principles and structures and understand the purpose of those structures; in social sciences they see patterns in the way that people behave and societies are formed and develop; in science they see patterns and structure in how matter is composed and chemical reactions take place; in music they learn to hear and compose chord patterns.
8. Look for and express regularity in repeated reasoning. In mathematics, students learn to notice if calculations are repeated, and look both for general methods and for shortcuts. They also learn to continually evaluate the reasonableness of their intermediate results. These skills can extend to other subjects. For example, when reading in any subject area, students learn to look for repeated reasoning in an author’s argument or in the ways different authors address a topic; when writing or orally expressing an argument or conclusion they can learn to make a habit of checking to make sure that their own reasoning is consistent.
I encourage you to think about how you can integrate these practices and thinking skills into your teaching and into students’ learning. Feel free to use and share this template to guide your own thinking or grade-level, department, or staff discussion. Enjoy!
This article first appeared on the Raising the Bar on Instruction blog and is posted here with permission. The Raising the Bar on Instruction website supports educators with instruction that aligns with the Common Core State Standards.
Posted on April 10, 2020