The common core standards are here and it’s time we start reflecting about the necessary changes that will be needed to meet these standards in the classroom. This blog is designed to first look at the mathematical practice and then to put into what the classroom should look like, feel like, and sound like. Teacher questioning will be critical to the success of the CCSS vision, so we will also explore this. If you are interested in this process to facilitate this discussion with your staff, read What Do the Common Core Standards Look Like in the Classroom.
1. Make sense of problems and persevere in solving them.
-Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals.
-They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt.
-They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution.
-They monitor and evaluate their progress and change course if necessary.
-Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem.
-Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, “Does this make sense?” They can understand the approaches of others to solving complex problems and identify correspondences between different approaches.
Explain, analyze, make conjectures, monitor, evaluate, check their answers.
So what does this really look like? The chart below is a work in progress. I’ve designed this with the expertise of many classroom teachers. If you have other ideas, please don’t hesitate to email me and share your expertise as well.
Mathematical Practice: #1 Make sense of problems and persevere in solving them.
|1. Be a math detective – Discuss the job of detectives, ” To look for clues/evidence and solve mysteries.”
2. Provide story problems and allow students to struggle with solutions.
3. Ask students to show three ways to solve the problem (Give individual think time prior to group)
4. Look at different student work (remove names and replace with Student 1 and Student 2) Ask, “what is this mathematician thinking or trying to figure out.”
5. Provide real world, high quality tasks.
6. Keep in mind the level of cognitive demand from this practice:
– Explain, analyze, make conjectures, monitor, evaluate, check their answers.
|“Struggling in mathematics is not the enemy any more than sweating is in basketball, it’s a clear sign you are in the game.” – Kim Sutton|