Drawing upon academic work and our own classroom-grounded research and experience, Math Solutions has identified the following four instructional needs as absolutely essential to improving instruction and student outcomes:
…to know the math they need to teach—know it deeply and flexibly enough to understand various solution paths and students’ reasoning.
It is completely natural for us to assume that different students will approach literature interpretation in different ways based on their background, knowledge, and experiences, yet when it comes to mathematics, we tend to expect all students to solve problems in exactly the same way. But as classrooms become more diverse, we need to become more flexible as educators in order to make math accessible for all students. This means knowing the content we teach deeply and flexibly enough to understand students’ reasoning and misconceptions—to be able to ask the right next question that facilitates and builds understanding.
… to understand the conditions necessary for learning, what they need to provide, and what students must make sense of for themselves.
In addition to having a firm grasp on content knowledge—the ‘what—we need to understand the “how” of learning mathematics. We need to know what information, such as academic language, we need to provide and what information students need to discover through constructive struggle. We need to understand the conditions necessary for students to really make sense of math for themselves.
…to recognize each student’s strengths and weaknesses, content knowledge, reasoning strategies, and misconceptions.
Understanding what students know is central to the process of teaching and learning. Assessment generally falls into two categories—summative (assessment OF learning) and formative (assessment FOR learning). To effectively plan and differentiate instruction, educators need to be able to acquire and interpret information about each student’s understanding and reasoning gained through listening, observation, examination and guided questioning.
… to have the expertise to make math accessible for all students, to ask questions that reveal and build understanding, and help students make sense of and solve problems.
Once educators know the content, the conditions for learning, and their individual students, they need the instructional strategies to make math accessible for each of their students. It’s understanding and choosing scaffolded, accessible tasks, asking the questions that reveal and build understanding, and providing the tools that will help students make sense of and solve mathematical problems.