*4. Content Knowledge* – The teacher uses content area knowledge, learning standards, appropriate pedagogy and resources to design and deliver curricula and instruction to impact student learning.

*4.1 Demonstrating Knowledge of Content and Pedagogy
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*Teacher’s plans and practice reflect familiarity with a wide range of effective pedagogical approaches in the discipline.*

*4.4 Designing Coherent Instruction in the area of Lesson and Unit Structure
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*The lesson or unit has a clearly defined structure around which activities are organized. Progression of activities is even, with reasonable time allocations.*

In order to plan successful math lessons, teachers should be familiar with a variety of pedagogical approaches in the discipline as well as understand the state standards for their curriculum. When reflecting on essential mathematics instructional practices, I agree with Ernst & Ryan (2014), that students should “interact in a safe, supportive learning community,” that teachers should “activate and build on [students’] prior knowledge,” that students should be led to “process information both visually and linguistically,” that problems should be solved with “meaningful contexts,” that students should “engage in reflection, self-monitoring, and metacognition,” and that students should “engage in complex thinking” (p. 17). In addition to following these guiding principles when planning curriculum, the mathematics teacher must also plan using the mathematical practices and standards that are appropriate for the given grade level, ensuring that the standards guide the design of their planning. Figure 1 illustrates how the Common Core State Standards (CCSS) are organized. These standards provide a guiding template to what needs to be learned but do not determine how students will engage with new knowledge. That is up to the district, school administration, and the teacher to determine. In addition, when designing math lessons, the eight standards for mathematical practice, as shown in the CCSS, should be applied to learning activities where applicable as well.

When designing lessons to meet the CCSS, it is important to use a backward design approach to planning. The teacher should be familiar with the standards and use them to guide their planning. Beginning with the domain, it is important to understand what students need to learn and what mathematical practices can be utilized for the activity being designed. For example, when focusing on 3.NBT as represented in figure 1, students should learn the three standards in the cluster underneath this activity. Moreover, rather than pull out some base ten blocks and have students complete a worksheet, it is essential that the lesson be structured around the CCSS standards, having students “…use place value understanding to round whole numbers to the nearest 10 or 100” or “…fluently add and subtract within 1000 using strategies and algorithms based on place value…” and so on. These standards will not be met in one lesson but rather, one or several units of curriculum should be designed and students need to be appropriately assessed to facilitate that the standards are met. Throughout the course of the school year, students should be able to practice and demonstrate all of the eight mathematical practices as well. When the teacher observes the class, they should recognize mathematical practices that students are struggling with and teach those practices further. For example, students may struggle with using grade appropriate vocabulary. In such a circumstance, the teacher may decide to incorporate a lesson where students practice communicating precisely to others while using appropriate academic vocabulary. Once the data reflects that the standards have been learned, students will be prepared for the next scaffolded step in their learning when they reach the fourth grade.

In addition to designing lessons around the standards, it is imperative that students are provided time to explore mathematics. When observing all of the guiding principles of essential mathematics instruction as document by Ernst & Ryan (2014), the concept of good teaching can be quite overwhelming. One practice that can help drive all of these principles is allowing students time to explore their learning, let them do the thinking during the course of the lesson. Figure 2 highlights a model that visually allocates the ideal time frame of a mathematics lesson.

While it is important to provide an introduction and time to summarize a lesson, students need time to think independently, utilize tools and classroom resources, work independently, work in cooperative groups, and explore different problems with increasing difficulty (Soine, 2015). The launch of the lesson, as shown in Figure 3, should be engaging and introduce material to prepare students for exploration.

Exploration time, as shown in Figure 4, should allow students to further engage in the material while the teacher circulates, assesses student learning, and asks questions to guide students to think more deeply about the material they are learning.

As shown in Figure 5, the lesson summary should provide the class with time to review the content they just learned. Students should be provided time to reflect on and share their learning with the class as well as provide feedback about the lesson (student voice) to their teacher. Too often, this smaller time span is overlooked, especially when lessons take longer than originally anticipated. Summarizing a lesson is incredibly important and should always be addressed.

Moving toward a time when I’ll be teaching in a classroom of my own, I plan to further familiarize myself with the CCSS and instructional practices that follow the guiding principles taught in this course. While Ernst & Ryan (2014) present many principles that pertain to mathematics instruction they are all relevant to all subjects taught in the classroom. Students should feel safe and secure, especially when sharing their thinking. Teachers should activate students’ prior knowledge and incorporate this into lessons. Students should be provided time to explore material in a variety of ways. Teachers should observe, assess, and question students so that they can develop deeper levels of meaning about the content they are learning when problem solving. Teachers should also allow time for students to summarize their learning, reflecting on what they learned. Lastly, curriculum should be designed around the standards, using a backward design approach to planning.

References:

Common Core State Standards Initiative (2015). *Common core state standards for mathematics.* (NGA Center and CCSSO, and NGA Center and CCSSO). Retrieved from http://www.corestandards.org/wp-content/uploads/Math_Standards.pdf

Ernst, K. & Ryan, S. (2014). *Your first years teaching elementary mathematics: Success from the start. *Reston, VA: The National Council of Teachers of Mathematics, Inc.

Soine, K. (2015, July 8). EDU 6130: *Lesson planning and reflection *[PowerPoint slides]. Retrieved from https://bbweb03.spu.edu/webapps/blackboard/content/listContent.jsp?course_id=_89224_1&content_id=_1076101_1