Here you will find information about the philosophy of the math curriculum, how it supports conceptual understanding, procedural fluency, and application, and resources available at the course level.
Our Philosophy
Every student is brilliant, but not every student feels brilliant in math class, particularly students from historically excluded communities. Research shows that students who believe they have brilliant ideas to add to the math classroom learn more.¹ Our aim is for students to see themselves and their classmates as having powerful mathematical ideas. In the words of the NRC report Adding It Up, we want students to develop a “productive disposition—[the] habitual inclination to see mathematics as sensible, useful, and worthwhile, coupled with a belief in diligence and one’s own efficacy.”²
We design our program to put students’ ideas at its center. We pose problems that invite a variety of approaches before formalizing them. This is based on the idea that “students learn mathematics as a result of solving problems. Mathematical ideas are the outcomes of the problem-solving experience rather than the elements that must be taught before problem solving.”³ Students take an active role (individually, in pairs, and in groups) in developing their own ideas first and then synthesize as a class.
This curriculum utilizes both the dynamic and interactive nature of computers and the flexible and creative nature of paper to invite, celebrate, and develop students’ ideas.
Digital lessons incorporate interpretive feedback to show students the meaning of their own thinking⁴ and offer opportunities for students to learn from each other’s responses⁵. Paper lessons often include movement around the classroom or other social features to support students in seeing each other’s brilliant ideas.
This problem-based approach invites teachers to take a critical role. As facilitators, teachers anticipate strategies students may use, monitor for those strategies, select and sequence students’ ideas, and orchestrate productive discussions to help students make connections between their ideas and others’ ideas.⁶
This approach to teaching and learning is supported by the teacher dashboard and conversation toolkit.
¹ Uttal, D. H. (1997). Beliefs about genetic influences on mathematics achievement: A cross-cultural comparison. Genetica, 99(2–3), 165–172. https://doi.org/10.1007/bf02259520
² National Research Council. (2001). Adding It Up: Helping Children Learn Mathematics. Washington, DC: National Academy Press. doi.org/10.17226/9822
³ Hiebert, J., Carpenter, T. P., Fennema, E., Fuson, K., Human, P., Murray, H., Olivier, A., & Wearne, D. (1996). Problem solving as a basis for reform in curriculum and instruction: The case of mathematics. Educational Researcher, 25(4), 12–21. https://doi.org/10.3102/0013189x025004012
⁴ Okita, S. Y., & Schwartz, D. L. (2013). Learning by teaching human pupils and teachable agents: The importance of recursive feedback. Journal of the Learning Sciences, 22(3), 375–412. https://doi.org/10.1080/10508406.2013.807263
⁵ Chase, C., Chin, D.B., Oppezzo, M., Schwartz, D.L. (2009). Teachable agents and the protégé effect: Increasing the effort towards learning. Journal of Science Education and Technology 18, 334–352. https://doi.org/10.1007/s10956-009-9180-4.
⁶ Smith, M.S., & Stein, M.K. (2018). 5 practices for orchestrating productive mathematics discussions (2nd ed.). SAGE Publications.
Conceptual Understanding, Procedural Fluency, and Application
Conceptual Understanding
We take every opportunity to build on students’ intuitions and knowledge to create new ideas.
Lessons develop students’ conceptual understanding by inviting them into familiar or accessible contexts and asking them for their own ideas before presenting more formal mathematics. In the Math 6 lesson Flour Planner, students reason about how many scoops they will need before learning procedures for fraction division. In the Math 8 lesson Turtle Crossing, students develop the concept of a function by creating their own graphs and watching the results.
Procedural Fluency
In order to transfer skills, students should be able to solve problems with accuracy and flexibility.
Several structures in the curriculum support procedural fluency: repeated challenges, where students engage in a series of challenges on the same topic, challenge creators, where students challenge themselves and their classmates to a question they create, and paper practice days that use social structures to reinforce skills before assessments.
Application
Students also have opportunities to apply what they have learned to new mathematical or real-world contexts.
Concepts are often introduced in context and most units end by inviting students to apply their learning, such as selecting transportation options or determining which container holds the most popcorn.
The lesson Movie Time invites students to use their knowledge of dividing by decimals to determine how long it will take to play a movie at different speeds.
Course Resources
Each course includes a Course Overview with resources to help teachers better understand the year as a whole.
In the Course Overview, you’ll find:
The Year at a Glance, a one-pager of the big ideas and standards for the year as well as a list of materials.
A Standards and Routines document that outlines which standard each lesson addresses and which lessons address each standard. It also includes which instructional routines are used throughout the year.
The Student Glossary, which contains illustrated examples of key vocabulary words from the entire year. In Amplify Desmos Math, the student glossary can be found on each unit page.
A Family and Caregiver Letter, which can also be found in both English and Spanish.
