Indicator C.2.2. Plan for Effective Instruction
Well-prepared beginning teachers of mathematics attend to a multitude of factors to design mathematical learning opportunities for students, including content, students' learning needs, students’ strengths, task selection, and the results of formative and summative assessments.
Careful and detailed planning is necessary to design lessons that build on students’ mathematical thinking while supporting development of key mathematical ideas. Well-prepared beginners realize that planning takes substantial amounts of time. They recognize the importance of having clear understandings of the mathematics content and mathematics learning goals for each unit and lesson as well as how these particular goals fit within a developmental progression of student learning (Daro, Mosher, & Corcoran, 2011). Well-prepared beginners are able to articulate and clarify mathematics learning goals during the planning process, knowing that the goals are the starting point that “sets the stage for everything else” (Hiebert, Morris, Berk, & Jansen, 2007, p. 57).
To provide effective instruction, one considers the prior knowledge and experiences students bring to a lesson and how the task will be set up or launched in meaningful contexts to ensure that each and every student has access to the content and contexts (Jackson, Garrison, Wilson, Gibbons, & Shahan, 2013). Therefore, well-prepared beginners strive to design classroom environments in which students have opportunities to communicate their thinking, listen to the thinking of others, connect mathematics to a variety of contexts, and make connections across mathematical ideas and subject areas. They plan purposeful and meaningful questions to probe student thinking, make the mathematics visible for discussion, and encourage reflection and justification (NCTM, 2014a).
In effective mathematics planning, teachers select meaningful tasks to motivate student learning, develop new mathematical knowledge, and build connections between conceptual and procedural understanding. Well-prepared beginners understand that providing students opportunities to think, reason, and solve problems requires cognitively challenging mathematical tasks (Stein, Smith, Henningsen, & Silver, 2009). Additionally, well-prepared beginners engage students on a regular basis with mathematical tasks that promote reasoning and problem solving, provide multiple entry points, have high ceilings to offer challenges, and support varied solution strategies (NCTM, 2014a). One can identify such tasks only by considering the ways in which students might solve them. Therefore, well-prepared beginners analyze tasks and lessons, anticipating students’ approaches and responses (Gravemeijer, 2004; Stigler & Hiebert, 1999). They understand that anticipating students’ responses involves considering both the array of strategies, both conventional and unconventional, that students might use to solve the task, and the ways those strategies relate to the mathematical concepts, representations, and procedures that students are learning (Stein, Engle, Smith, & Hughes, 2008).
Well-prepared beginners attend to the needs of their students in their planning of lessons and units. That is, in their lesson planning, the beginners incorporate inclusive and equity-based teaching practices. Formative assessment is an integral aspect of effective instruction; therefore, lesson planning must include a plan for monitoring and assessing student understanding (Black & Wiliam, 1998). Well-prepared beginners have repertoires of strategies to elicit evidence of students’ progress toward the intended mathematics learning goals, such as being able to use observation checklists, interviews, writing prompts, exit tickets, quizzes, and tests. They realize that although they have anticipated student responses, the evidence from these assessments may require a departure from the planned lesson or may affect subsequent lessons within a unit of study. They also recognize their responsibilities to develop interventions to support the students who are not reaching the objectives of the grade-level instruction. Knowing the importance of monitoring and attending to the progress of students who are struggling to learn, the well-prepared beginning teacher uses results from formative assessments to design targeted instruction presented outside the regular grade-level mathematics session.