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In an effective mathematics classroom, an observer should find that the teacher is (Protheroe, 2007): Demonstrating acceptance of students’ divergent ideas. The teacher challenges students to think deeply about the problems they are solving, reaching beyond the solutions and algorithms required to solve the problem.
- Knowing the Learner and the Curriculum
- Creating a Positive and Safe Learning Environment
- High-Impact Instructional Practices
- Learning Goals, Success Criteria, and Descriptive Feedback
- When students are beginning to learn about a concept, success criteria should:
- As students progress with their learning, success criteria should:
- When students are deep in the learning process, success criteria should:
- Direct Instruction
- When students are beginning to learn about a concept, direct instruction should:
- As students progress with their learning, direct instruction should:
- When students are deep in the learning process, direct instruction should:
- When students are beginning to learn about a concept, problem-solving experiences should:
- As students progress with their learning, problem-solving experiences should:
- When students are deep in the learning process, problem-solving experiences should:
- Teaching about Problem Solving
- When students are beginning to learn about a concept, teaching about problem solving should:
- As students progress with their learning, teaching about problem solving should:
- When students are deep in the learning process, teaching about problem solving should:
- Tools and Representations
- When students are beginning to learn about a concept, tools and representations should:
- As students progress with their learning, tools and representations should:
- When students are deep in the learning process, tools and representations should:
- Math Conversations
- As students are beginning to learn about a concept, effective conversations should:
- As students progress with their learning, effective conversations should:
- When students are deep in the learning process, effective conversations should:
- Small-Group Instruction
- When students are beginning to learn about a concept, small-group instruction should:
- As students progress with their learning, small-group instruction should:
- When students are deep in the learning process, small-group instruction should:
- Deliberate Practice
- When students are beginning to learn about a concept, deliberate practice should:
- As students progress with their learning, deliberate practice should:
- When students are deep in the learning process, deliberate practice should:
- Flexible Groupings
- When students are beginning to learn about a concept, flexible groupings should:
- As students progress with their learning, flexible groupings should:
- When students are deep in the learning process, flexible groupings should:
Effective instruction in all subjects requires that educators know their students, including their learning needs and strengths, their backgrounds and circumstances, and their social and personal identities. Teachers also need to be aware of their own “social location” – that is, who they are in terms of gender, race or ethnicity, socio- economic ...
Effective math instruction must be supported by an inclusive, positive, and safe learning environment, where students feel valued and engaged. To establish such an environ-ment, educators inform students what is expected of them and how the classroom operates. When an assumption is made that students already know what is expected of them, ongoing i...
The thoughtful use of high-impact instructional practices – including knowing when to use them and how they might be combined to best support the achievement of specific math goals – is an essential component of effective math instruction. This resource focuses on practices that researchers have consistently shown to have a high impact on teaching...
While some high-impact practices may be used on an as-needed basis, it is always important to provide students with learning goals and success criteria. This is an essential practice for effective instruction. Learning goals and success criteria outline the intention for the lesson and how this intention will be achieved. When educators and stude...
define the terms or vocabulary to be used capture key mathematical concepts as they emerge in the classroom
define the learning goal in student-friendly language capture key mathematical concepts as they emerge in the classroom demonstrate necessary conventions
define what successful attainment of learning goals looks like make connections to other strands or content areas promote self-reflection
Direct instruction is a concise, intentional form of instruction. It uses clearly communi-cated learning goals, introduces models and representations in context, and incorpo-rates questioning and brief activities. It verbalizes thought processes, defines and uses math vocabulary, and makes key concepts and connections explicit. Direct instruction c...
activate prior knowledge and introduce new vocabulary highlight key mathematical ideas from previous student work connect different representations and strategies model how to use manipulatives or representations
reinforce procedures, or help students use more efficient procedures highlight or introduce mathematical conventions
highlight connections between tasks, strategies, representations, and concepts encourage metacognition or thinking about one’s own thinking. When students are invited to think about and monitor their own thinking, they will develop a measure of “reasonableness” in their work that will enable them to evaluate it. Such metacognitive skills may not ...
activate prior knowledge and be relevant to students’ lived experiences offer multiple entry points and involve multiple solutions and/or solution strategies
support student-generated procedures and invite students to choose an effective strategy provide an opportunity to represent thinking using concrete or pictorial models
offer multiple entry points, involve multiple steps, and require justification of thinking invite students to compare and contrast tasks involve connections to other strands and content areas (e.g., cross-curricular applications of STEM) to support a transfer of learning
Teaching students about the process of problem solving makes explicit the thinking that problem solving requires. It helps students to engage in “self talk”, which they can use when facing a novel problem. It also helps students to understand the overall structure of a problem, and reinforces that problem solving requires perseverance and that a g...
focus on helping students to understand the problem by first recognizing what information is provided and what it is they are being asked to do explore the underlying structure of problems discuss mistakes as an important part of learning
focus on using effective representations to model the problem-solving situation highlight strategies to explain thinking and justify solutions highlight underlying structures or types of problems discuss perseverance as a necessary part of problem solving and learning
involve comparing and contrasting problems to support students in recognizing the structure of each problem and in being able to generalize about problems and see beyond “today’s” problem invite students to reflect on their learning, the strategies they used, and the “self talk” that helped them solve problems
The use of tools and representations supports a conceptual understanding of math-ematics at all grade levels. Chosen carefully, tools and representations provide a way for students to think through problems and then communicate their thinking. Tools and representations explicitly and visually represent math ideas that are abstract. When paired with...
connect to prior knowledge and students’ lived experiences model situations concretely or pictorially model student thinking
be introduced to model situations in new ways be connected to other tools and representations include those that will be appropriate for future problems (e.g., those that will work with larger numbers or that can be transferred to other situations)
model situations concretely, pictorially, or abstractly, as is developmentally appropriate be compared and contrasted with other representations
Effective math classrooms provide multiple opportunities for students to engage in meaningful math talk. Conversations about math build understanding as students listen and respond to their classmates’ expression of mathematical ideas. Students may share their ideas with a partner or within a small group, in the context of whole class discussions...
activate prior knowledge and connect the current task to previous learning (“How is this like something you have done before?”) gather information about students’ current level of understanding and ways of knowing (“How can you show your thinking?” “What math words can describe this?”)
make math explicit (“How have you shown your thinking?”) probe thinking and require explanations (“How could you explain your thinking to someone just learning this?” “How do you know?” “Why did you represent the problem this way?”) reveal understanding and/or misconceptions (“How did you solve this problem?” “Where did you get stuck?”)
support connections and transfer to other strands/content areas (“Where can you see this math at home? In other places?” “What other math connects to this?”) require justifications and/or explanations (“Would this always be true? How do you know?”) promote metacognition (“What was the most challenging thing about this task?” “What would you do di...
encourage reflection and connections between mathematical concepts consolidate and confirm learning
encourage reflection and connections between mathematical concepts consolidate and confirm learning
encourage reflection and connections between mathematical concepts consolidate and confirm learning
encourage reflection and connections between mathematical concepts consolidate and confirm learning
encourage reflection and connections between mathematical concepts consolidate and confirm learning
encourage reflection and connections between mathematical concepts consolidate and confirm learning
encourage reflection and connections between mathematical concepts consolidate and confirm learning
encourage reflection and connections between mathematical concepts consolidate and confirm learning
encourage reflection and connections between mathematical concepts consolidate and confirm learning
encourage reflection and connections between mathematical concepts consolidate and confirm learning
encourage reflection and connections between mathematical concepts consolidate and confirm learning
encourage reflection and connections between mathematical concepts consolidate and confirm learning
paring student approaches. nd arguments.Pose purposeful questions. Effective teaching of mathematics uses purposeful questions to assess and advance students’ reasoning and sense making about import. nt mathematical ideas and relationships.Build procedur. l fluency from conceptual understanding. Effective teaching of mathematics builds ...
area of effective mathematics instruction. Belief 5: Effective mathematics instruction occurs when instruction is supported by the community, through the cooperation of instructional leaders at both the school and board levels, of parents, and of other members of the community at large. Effective math instruction does not occur in isolation.
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Jun 5, 2024 · 6: Differentiated Instruction. Differentiated instruction is the cornerstone of effective instructional practice for all students. This instructional strategy is based on the idea that different students need different approaches, different types of practice, and varied amounts of time to achieve the same learning goals.
To improve student mathematics performance, more and more school and districts have implemented high-quality mathematics instruction. This instruction involves the implementation of both: A standards-based curriculum — The concepts and skills believed to be important for students to learn.
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based instruction, educators found that a careful and intensive review of research revealed the importance of using a combination of both approach-es. Similarly, there are at least two camps prominent in the discussion of how math should be taught. The two teaching approaches have clear differ-ences. In skills-based instruction, teach-
