By the end of a PST, students should possess a clear understanding of how to solve that. particular problem as well as t
Math Instruction at Brooke
Brooke’s math curriculum is designed to teach students to understand math at the conceptual level. A conceptual understanding of math will enable students to think flexibility and logically so they can use what they know to solve new and challenging problems. Starting in kindergarten, we teach students to embrace the struggle of problem solving in order to normalize the difficulty they will undoubtedly face, at times, when searching for solutions. We believe that students need extended amounts of time each day to struggle with challenging math problems. Students also need time to articulate their strategies and solutions and listen to their peers do the same. These vital skills are strengthened every day through problem solving tasks (PSTs). During PSTs, students grapple independently with a single, difficult math problem. Then, teachers moderate a discussion by pushing students to share their solutions using relevant, specific vocabulary, by posing clarifying questions and, when necessary, by summarizing key takeaways. Teachers also step in to address misconceptions or refocus the discussion if students get off track. By the end of a PST, students should possess a clear understanding of how to solve that particular problem as well as the contextual and conceptual knowledge necessary to tackle similar ones. Following a PST, students practice a variety of problems independently or with a partner. Some of the practice problems relate to the problem solving task of the day, while others review previously learned content. Mixed review further promotes the fluid and flexible thinking we want our students to develop. Mental math and fact power are two other important components of the elementary math curriculum. In mental math, students solve challenging problems without using algorithms or other paper-based strategies. This promotes the number sense that will enable students to attack challenging problems more efficiently and logically. For example, a second grade teacher may ask students to add 90 + 14, even before they know how to use an algorithm with regrouping. A student can solve this mentally by decomposing the number 14 into 10 and 4, adding 10 to 90 to make 100 and then adding 4 to get 104. Fact power involves the memorization of facts to promote automaticity. In first grade, student learn basic addition and subtraction facts through 10. In second grade, they learn doubles addition facts up to 25. In third grade, they learn division facts through 10. And in fourth grade, they learn fraction to decimal conversations. Students need to know basic arithmetic facts backwards and forwards in order to handle the more rigorous work they do in PSTs, logic and mental math. Fluency with basic facts frees up mental energy to focus on more complicated parts of problems and aids students in all areas of math work. Logic stories occur at a separate time throughout the day. During this block, students solve a challenging, multistep problem that might draw upon content learned previously that year or even in previous grades. Logic stories require that students decipher between important and superfluous information, use models to ground their thinking and follow a reasonable line of thinking that leads to a solution. Middle school students do not have a set time of day for logic stories and mental math. However, they do have an Applied Math block, which is a more advanced variation of logic stories. The math curriculum prepares students to embrace and even celebrate the struggle of solving challenging problems. Each year, students grow more and more confident in their ability to reason their way through math class and learn to see themselves as logical and capable thinkers. We think the development of this identify is a crucial step towards building a life-long love for and proficiency with mathematical thinking.
