vmt-award-2024_47--2-_purple

cause it tells the student which operation to use. The students solve the problem by implementing a procedure correctly. Task C is a higher - level task because it has multiple entry points and students are encouraged to use a variety of representations. Use the following guidelines to help you recognize a higher - level task, as seen in Task C:

Ed.). NCTM.

How do we implement meaningful classroom discussions based on higher level tasks?

Smith and Stein's (2019) 5 Practices for Orchestrat ing Productive Mathematics Discussion, is ground ed on high cognitive demand mathematical tasks and a well thought out and thorough lesson plan. The book discusses the five practices and shows how they are woven into a lesson plan based on the Thinking Through a Lesson Protocol (TTLP) (Lewis, 2002; Sigler & Hiebert, 1999). The lesson plan becomes the framework for the enacted math ematics lesson. Smith and Stein ’ s (2019) 5 Practic es include: anticipating, monitoring, selecting, se quencing and connecting. Now, let us take a deeper look at each practice. During the lesson planning stage and after a high cognitive demand task is selected, , stop and think about all the ways students might approach the task. Brainstorm possible strategies and misconcep tions that students may use when solving the task. By anticipating their strategies and possible mis conception, will prepare you to use questions to guide students during the task. You will want to ask students a variety of questions based on your observations of their problem solving strategies to elicit their thinking to ensure the mathematics les son goals are met. The authors provide clear examples that highlight the type of question you may use. For example, assessing questions help you understand a student's thinking, while advancing questions help to drive students ’ thinking further towards the mathematics goal. Preparing these types of questions in advance will help you keep the class focused and engaged. Figure 2, below, has examples of different types of questions you could ask students using Task C from Figure 1. Anticipate: What strategies do you think stu dents will use?

● Does the task have multiple entry points?

● Does the task have the student make connections to concepts or representations?

● Does the task promote the students to think and use their reasoning skills?

● Are there varied solution strategies that can be used to solve?

● Can I modify a task I already use to make it more cognitively demanding?

● Does the task align to the goal of my lesson?

Different tasks provide different opportunities for student learning and the low level tasks have their place. Low level tasks ask students to perform a memorized procedure in a routine manner, which is one type of student thinking, fluency with math facts, algorithms or procedures; tasks that demand engagement with concepts that stimulate students to make connections lead to a different set of op portunities for student thinking, ability to think deeply about the mathematical concepts (Smith and Stein, 2018). Implementing high - level tasks pro vide the foundation for meaningful mathematics discussions. (For more information about cognitive demand and tasks, see Stein, M.K., Smith M.S., Henningsen, M.A., and Silver, E.A. (2009). Imple menting Statards - Based Mathematics Instruction: A Casebook for Professional Development. (2nd

Monitor: What are my students thinking?

Figure 1: Tasks A, B, and C

Virginia Mathematics Teacher vol. 47, no. 2

51