The New Art and Science of Teaching Mathematics. Robert J. Marzano

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      Source: National Governors Association Center for Best Practices & Council of Chief State School Officers, 2013.

Figure 1.2: Learning progression for mathematics, secondary level.

       Clearly Articulating Learning Goals

      Mathematics learning goals are most effective when teachers communicate them in a way students can clearly understand; however, students must also feel as though they “own” the goals. Student ownership is the process of allowing students the freedom to choose their goals and take responsibility for measuring their progress toward meeting them. Student ownership occurs most effectively when students are able to connect to mathematics using natural, everyday language. Stephen Chappuis and Richard J. Stiggins (2002) explain that sharing learning goals in student-friendly language at the outset of a lesson is the critical first step in helping students know where they are going. They also point out that students cannot assess their own learning (see element 2, tracking student progress, page 18) or set goals to work toward without a clear vision of the intended learning. When they do try to assess their own achievement without understanding the learning targets they have been working toward, their conclusions can’t help them move forward.

      The following three actions will help teachers communicate learning goals effectively so that students can connect to mathematics.

      1. Eliminating jargon: Eliminate jargon that is intended for the teacher and instead incorporate empowering language that provides focus and motivation.

      2. Making goals concrete: Communicate learning goals with vivid and concrete language.

      3. Using imagery and multiple representations: Promote mathematics concepts as visually connected to numerical values and symbols.

      Table 1.1 provides some examples of these three actions.

Table 1.1: Actions for Communicating Learning Goals

      Eliminating Jargon

      Learning goals can be difficult for students to grasp when they contain pedagogical jargon and seem to be crafted more for education experts than for students. We don’t mean to discredit the use of academic language; however, when academic language becomes a barrier because it prevents students from connecting with the material, teachers have to re-evaluate how they’re communicating about mathematics. When learning goals are ambiguous, they don’t provide the focus, motivation, or inspiration students need to reach targets. Mathematics teachers must align learning goal language to desired learning outcomes for students using everyday language and connect it to academic language by showing the students the goal written in various ways. Judit Moschkovich (2012) states that instruction needs to move away from a monolithic view of mathematical discourse and consider everyday and academic discourses as interdependent, dialectical, and related rather than assume they are mutually exclusive. Additionally, learning goals should make appropriate connections to academic language when scaffolding is present. Figure 1.3 shows a standard followed by the rewritten student-friendly, jargon-free statement for two grade levels and algebra II.

Figure 1.3: Transforming a learning goal by eliminating jargon.

      Obtaining student feedback is the best way to determine if learning goals make sense to students. Creating a focus group of students (a committee to eliminate jargon) that vet learning goals is a strategy to ensure your learning goals are student friendly. In this process, the teacher asks students in the focus group to circle nouns and verbs that seem ambiguous or don’t seem very connected to everyday language.

      Figure 1.4 is an example of how a student focus group would provide feedback on the first draft of a learning goal.

Figure 1.4: Transforming a learning goal with student feedback.

      The students from the group in figure СКАЧАТЬ