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3.1 Contrast and describe approaches to problem solving
3.1 Contrast and describe approaches to problem solving
Students should be encouraged to learn through problem solving. As a teacher, we should ensure success in every student by focusing numbers 1-8 on Table 3.1.
Benefits to Teaching Problem Solving to Students:
1. Enhances Understanding: Students integrate new concepts with existing knowledge, improving comprehension.
2. Develops Mathematical Practices: Students actively engage in math, developing essential skills.
3. Boosts Confidence and Identity: Encourages students to see themselves as capable mathematicians.
4. Builds on Students’ Strengths: Students use their preferred strategies, enhancing learning.
5. Allows for Extensions: Offers challenging questions for all students, including advanced learners.
6. Reduces Discipline Issues: Engages students, reducing boredom and misbehavior.
7. Provides Assessment Data: Gives teachers insights into students' understanding and misconceptions.
8. Encourages Creativity: Promotes inventive problem-solving, highlighting diverse student thinking.
3.2 Roles of Problem-Solving and Learning progression in setting Goals For student learning
3.2 Roles of Problem-Solving and Learning progression in setting Goals For student learning
Creating a clear visual definition of goals for learning mathematics lessons starts with using the mind to think of goals needed in an evolving society. As a result, the visual and conceptual learning maps that describe how students develop their understanding of a subject area over time can aid with setting goals for student learning. Generating an end goal specification will produce the result for the start of goal setting in general. Life skills in critical thinking, communication, collaboration, creativity, and use of technology effectively are developed more when learning mathematics. Problem-solving has been a segment of mathematics learning regularly, and the use varies based on the goals set for the students. The three vital approaches to problem-solving are teaching for problem-solving, teaching problem-solving, and teaching through problem-solving.
A problem can be solved by modeling or describing the problem mathematically for a situation that is in reality to solve the problem or the question in the problem-solving. Therefore, learning goals must fit within learning progressions. Learning progressions describe the development of the student's thinking and strategies over time in terms of sophistication of both conceptual understanding and procedural fluency (Clements & Sarma; 2021; Daro, Mosher, & Corcoran, 2011; Siemon et al., 2017; Sztajn, Confrey, Wilson, & Edgington, 2012). As previously stated, creating a clear visual definition of goals for learning mathematics lessons starts with using the mind to think of goals needed in an evolving society it's vital. Ask yourself how the topics relate to the student's prior mathematics knowledge and experience. Also, how does the idea connect to future mathematics learning the students may experience?
Van de Walle, J. A., Karp, K. S., & Bay-Williams, J. M. (2022). Elementary and middle school mathematics: Teaching developmentally. Pearson. One Lake Street, Upper Saddle River, New Jersey 07458.
3.3 Critiquing Mathematical Tasks
3.3 Critiquing Mathematical Tasks
Teachers must choose tasks and activities that are problematic and "promote problem - solving."
Teachers must choose tasks and activities that are problematic and "promote problem - solving."
To achieve this, tasks should:
To achieve this, tasks should:
- provide a question where there is no one method for solving it
- be free of having one "correct" solution to the problem
How to Adjust Your Tasks to Make Them More High Level & Problem Solving:
How to Adjust Your Tasks to Make Them More High Level & Problem Solving:
Allow more than one way/strategy
Let students explore
Begin with students' intuition before teaching the conventional' method
Add visuals
Help students see what they already know
Let students attempt to convince each other and ask clarifying questions
Common Tasks that are Low Level Cognitive Demand:
Common Tasks that are Low Level Cognitive Demand:
Memorization: these are routine, involve reproducing previously learned information, students are not required to make connections to related concepts.
Drill Tasks & Problems: receptive exercises that repeat a specific procedure, does not promote conceptual understanding
Tasks with High Level Cognitive Demand Have:
Tasks with High Level Cognitive Demand Have:
Multiple Entry + Exit Points
The task can be approached in various ways to promote diversity of thought. Tasks can also be solved in various ways.
Relevant Context
The problems in the tasks should center around things students care about.
Use Literature
Read different books that incorporate math into the storylines.
Connect to Other Disciplines
Connect other subjects such as Science and Social Studies to math tasks. Students will understand the "interconnection" between the concepts they're learning.
Ways to engage student discourse
Ways to engage student discourse
SECTION 3.4
It's imperative that students learn how to talk through their mental math processing, espcially English language learners. The verbal practice will help them with their vocabularly, language acquisition, and math reasoning.
Teachers need to ask questions and structure the lesson to prompt dialogue and student talk
Teachers need to ask questions and structure the lesson to prompt dialogue and student talk
5 teacher actions define this process: Anticipating, monitoring, selecting, sequencing, and connecting. This all refers to the choices teacher make it what mathematical concepts to introduce, the order they'll be taught in, and how to connect them.
The goal is to unveil student thinking and have them understand one anothers' thinking. Teachers should be careful not to control, interrupt or manipulate student discourse.
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