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A. Different ways to implement Approaches to Teaching 

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A. Different ways to implement Approaches to Teaching 

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1. Inquiry-Based Learning

Encourage students to ask questions and investigate mathematical concepts through guided discovery rather than direct instruction. For example, present a real-world problem and have students explore which math concepts apply and why.

2. Use of Visual Aids and Manipulatives

Incorporate graphs, diagrams, dynamic geometry software (like GeoGebra), and physical models to help students visualize abstract ideas and see connections between concepts.

3. Concept Mapping

Have students create concept maps that connect new ideas with prior knowledge, showing relationships and hierarchies between mathematical concepts.

4. Collaborative Learning

Organize group work where students explain concepts to each other, solve problems together, and challenge each other’s understanding, fostering deeper conceptual grasp.

5. Reflection and Metacognition

Integrate journaling or short writing prompts where students reflect on their understanding of concepts, explaining “why” and “how” rather than just “what.”

6. Problem-Solving Tasks Focused on Reasoning

Design problems that require justification, explanation, and exploration of multiple solution methods, promoting conceptual clarity.

7. Real-World Applications

Connect math concepts to real-life situations, showing relevance and helping students build mental models grounded in practical examples.

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B. Focused on conceptual understanding understanding in your math classroom:

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B. Focused on conceptual understanding understanding in your math classroom:

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1. Teaching through Inquiry

How it works: Instead of starting with formulas, I pose real-life or open-ended questions ("How can we model population growth?").

Why it’s effective: It fosters curiosity, deepens understanding, and helps students make connections between mathematical models and real-world contexts, especially useful in IB and AP courses where application is key.

2. Developing Independent Learners

How it works: I use structured scaffolds like math journals, IA progress trackers, and DeltaMath to gradually build autonomy.

Why it’s effective: Students take ownership of their learning, develop self-management ATL skills, and become confident in exploring mathematical challenges on their own skills needed for IA and HL Paper 3 success.

3. Emphasizing Conceptual Understanding

How it works: I prioritize why a method works before how to using visual models, collaborative activities, and technology tools (e.g., Desmos, GeoGebra).

Why it’s effective: Students don’t just memorize formulas, they understand underlying principles, which leads to flexible thinking and better performance on unfamiliar problems.

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C. Three ways this approach can effectively work in my mathematics classroom:

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C. Three ways this approach can effectively work in my mathematics classroom:

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1. School: International School of Toulouse, Toulouse, France. Subject: Mathematics lessons

Critical Thinking skill and problems solving exploration skill

Students to explore, struggle, and discover strategies and solutions independently or collaboratively before being taught formal methods. Analyze and evaluate problems, generate new ideas and solutions, Reflect on processes and outcomes, Apply knowledge in unfamiliar contexts, these are central to inquiry-based and concept-driven learning.

2. School: Colegio de San Francisco de Paula, Sevilla, Spain. subject: Mathematics lesson

Communication skill: Student-led Discussions:

Students present their solutions or statistical analyses use technology, fostering critical thinking, communication skills, and peer-to-peer learning.

3. School: Branksome Hall, Toronto, Canada. DP subject: Chemistry lesson

Self-Management skills: As a mathematics educator, I see Self-Management skills as essential for student success, especially in courses like IB Math, Calculus, and  Statistics. These skills allow students to take ownership of their learning, manage complex tasks, and develop persistence in problem-solving.

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A- Describe three ways in which you can see the assigned approaches to teaching (conceptual understanding) working well in your mathematics classroom:

1. Justifying Thinking
In the video from UNIS in New York, students had to explain and justify their reasoning with pedigree charts. I can see this working really well in my maths classroom by getting students to talk through their methods and explain why each step makes sense, like when solving algebra problems or working through equations. It helps shift the focus from just getting the right answer to actually understanding how and why the method works.

2. Using Real-World Problems to Connect Concepts
The Toronto French School video showed students using a real-life case study to tie together different biology concepts. In maths, I’d use a similar approach by giving students real-world scenarios, like budgeting, planning a trip, or designing a space, where they need to apply multiple maths skills (e.g. percentages, measurement, ratios). It helps students make connections between topics and see how maths actually applies outside the classroom.

3. Group Discussions and Comparing Strategies
In the Munich video, students worked in teams to debate and explore different perspectives. I think this would be great in maths too. I’d have students solve a problem in groups, then compare their strategies and explain why one method might be better than another. These conversations can help students catch misunderstandings and learn different ways to approach a problem, which builds their overall understanding.

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B- Describe three ways in which you can implement "conceptual understanding" in your mathematics classroom:

1. Get students to explain why a method works
Instead of just teaching students how to solve a problem, I’d regularly ask them to explain why they’re using a certain method, and what each step means. For example, when solving equations, they could describe why we do the same thing to both sides or what isolating a variable really means. This helps them understand the logic behind the process — not just how to follow steps.

2. Use real-world problems that combine multiple concepts
I’d give students tasks that reflect real-life situations and require more than one maths skill to solve. For example, a project where they plan a party budget might involve percentages, addition, subtraction, and unit conversions. This helps them see how different topics connect and how maths actually applies to life — which builds stronger, more meaningful understanding.

3. Encourage discussion and comparing strategies
I’d often have students work in pairs or groups to solve problems, and then talk about their different methods. Getting students to explain their thinking to each other and see multiple ways to reach the same answer encourages flexible thinking. It also helps them break down and understand the concepts behind the solutions — not just copy the answer.

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Conceptual understanding (Ingatestone)

Teacher let Ss explore the concept of causation by investigating different statements of causes

Ss see how causes can be classified into themes

From their, Ss see that causation can have different was of viewing and can be extended in different subject areas

Conceptual understanding (Bangplee)

Ss look at patterns in a poem

Ss analyse using two different approaches reader response vs structure

Ss connect their learnings in different areas

3 ways this can work well in mathematics classroom

Ss can build and explore the concepts rather than being told about the concepts, which can help them gain a deeper understanding and appreciate the concepts more

Ss can see that learning is not linear, but it's about recognising patterns, testing their hypothesis and justify their understanding and therefore more engaging and they know that learning is complex, not an easy and straight forward process.

Ss can see that by working together, they can create knowledge much faster.

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C- Three approaches to implement conceptual understanding in my mathematica classroom

1. Use Real-Life Contexts and Visual Representations
To support conceptual understanding, I would aim to link mathematical concepts to real-life situations wherever possible. For instance, I might use visual tools like number lines, arrays, or bar models to help students make sense of abstract ideas. By seeing how math works in practical or visual ways, students would be more likely to understand the underlying concepts rather than just memorising steps.

2. Encourage Mathematical Discussions and Student Reasoning
I would strive to create a classroom environment where students feel confident explaining their thinking and exploring different strategies. Activities such as “Think-Pair-Share” or group investigations could be used to encourage students to verbalise their reasoning. This would not only strengthen their own understanding but also allow them to learn from one another.

3. Connect New Concepts to Prior Knowledge
Whenever introducing a new topic, I would try to connect it to something students already know. For example, I might begin a lesson on algebra by referring back to familiar ideas like number patterns or basic arithmetic. This approach would help students see the links between topics and develop a more coherent and connected understanding of mathematics.

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1. Teaching Through Inquiry

Description:

Encourages students to explore, ask questions, and discover mathematical relationships on their own or in groups.

Classroom Strategies:

Use real-world problems that require students to model or interpret data.

Pose open-ended questions:

➤ “What patterns do you notice?”

➤ “Can you find more than one solution?”

Allow students to generate conjectures before teaching rules or theorems.

Example Activity:

Investigate whether the sum of two odd numbers is always even. Justify your conclusion algebraically and with examples.

Benefits:

✔ Promotes curiosity and mathematical thinking

✔ Builds ownership of learning

✔ Prepares students for unfamiliar, higher-level problems

2. Teaching Focused on Conceptual Understanding

Description:

Focuses on “why” behind mathematical ideas to build meaningful understanding and connections.

Classroom Strategies:

Use multiple representations (e.g., graphs, tables, diagrams, algebra).

Discuss the reasoning behind formulas and algorithms.

Encourage students to explain their thinking to peers.

Example Activity:

Use area models to explain how the distributive property supports polynomial multiplication.

Benefits:

✔ Supports transfer of knowledge

✔ Strengthens long-term retention

✔ Encourages deeper, cross-topic learning

3. Teaching that Develops Learner Profile Attributes

Description:

Math lessons are designed to build IB learner profile attributes like inquirer, thinker, risk-taker, and reflective.

Classroom Strategies:

Provide challenging tasks that require creative thinking and resilience.

Use group work to promote communication and collaboration.

Integrate reflective journals or exit tickets:

➤ “What challenged you today?”

➤ “What strategy would you try next time?”

Example Activity:

Students attempt a complex modeling problem, then reflect on how they collaborated and approached it, even if they didn’t find a complete solution.

Benefits:

✔ Builds student confidence and risk-taking in math

✔ Encourages critical self-reflection and goal-setting

✔ Supports the development of global, lifelong learners