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One teaching strategy that was mentioned in the text is the choral counting which involves counting in a structured way. The teacher selects a starting number, an interval, and the counting direction. For an example, starting at 8 and counting up by tens or starting from 12:00 and counting up by 20 minutes. The teacher writes these numbers on the board so that students visually see the patterns that are being counted together. In the classroom, students would count out loud as the teacher records each number on the board. While doing this, they observe patterns, make predictions, and reason about why these patterns occur. From here on, the teacher can ask further questions like "if we kept counting what would the next number be" or "what do you notice about the numbers in each column.

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A teaching strategy that could be used in the classroom to promote mathematical reasoning is a think-pair-share or round-robin activity. These types of activities allow students to be able to think on their own about the problem they were given, come up with a solution on their own, share it with a partner or table group, and then receive feedback from other students by sharing it with the whole class or a bigger group of people. These activities can engage students in their thinking, allowing them to see what their classmates are thinking. In the classroom, the teacher would pose a problem or something for students to think about, and ask them to share with a partner/table group. While the sharing is going on the teacher can walk around the room and scaffold the students if needed. Then, the teacher can lead the class in a whole group discussion about said topic, and students can develop more and more ideas from hearing the ideas from their classmates.

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A teaching strategy that promotes reasoning could be discussion. This could be done in partners or as whole class discussions. In the classroom, students would work on their math problem on their own and then at the end everyone would come together to talk about what they got and how they came up with that answer. As students engage with others they learn new methods and learn about their own thinking. Students are having to explain their thinking and it makes them think of how they solved it and maybe any mistakes that could’ve been done along the way. Students get practice with defending their own ideas and become confident in their strategies as they learn from others.

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A teaching strategy used to promote mathematical reasoning in the classroom is to make personal connections with the student's lives and mathematics in order to motivate students to learn math and show how valuable it is outside the classroom. Other strategies include sharing in class discussions and allowing students to demonstrate their thinking strategies and pull ideas from each other, learning new strategies and other ways to reason mathematically.

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One effective teaching strategy to promote mathematical reasoning is using open-ended questions and tasks. These questions encourage students to explore multiple solution paths, justify their reasoning, and engage in discussions around various approaches. By asking open-ended questions to various problems, students may be able to notice patterns. In the text, they talk about noticing patterns, and list a variety of questions teachers can ask the students to get them thinking about their answers, and other ways they could solve the problems. Open-ended questions allows students to not just solve problems, but gets them to actively reason, and reflect on their problem solving process(es).

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A teaching strategy you can use to promote mathematical reasoning in an elementary classroom is asking open-ended questions. Instead of only finding the answer, students explain why they chose certain methods and how they got their solutions. For example, after solving a problem, the teacher could ask, "Can you find another way to solve this?" or "What would happen if we changed this number?" In the classroom, students could work in pairs or small groups, talking about their ideas and listening to others. Teachers can use tools like number lines or counters to help students explain their thinking. Giving students time to reflect and discuss with each other builds a sense of teamwork and shows that reasoning is important. This approach helps students feel more confident in math and strengthens their understanding.

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A strategy to promote mathematical reasoning is by using real-world problems. You can pick a math topic, like fractions or percentages, and connect it to a situation students can relate to, like planning a pizza party and figuring out how much food to buy/how to split it up. Then, let them work on the problem alone or in small groups, and afterward, have a class discussion where they share their solutions and explain their thinking. This approach helps students see how math is useful in everyday life and makes learning more interesting and hands on.

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A teaching strategy that was mentioned in the chapter was choral counting. This is an activity where the teacher leads the class in counting aloud together and following a specific pattern. The teacher will decide the starting, ending, and pattern. Students will respond by calling out the next number in the sequence as a class. This activity promotes pattern recognition by having the students listen and participate in the counting. They will be able to notice things like repeating digits, or relationships between the numbers. To implement this in the classroom, you can do this activity with your class and then lead a discussion about what was learned and how this can be useful in everyday life.

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A strategy I would like to use within my classroom would be creating real-world activities/lessons that are applicable to students' real lives. Incorporating these types of activities will increase student engagement as these activities are viewed as more applicable to students. This can be done in many different ways, creating a word problem that uses students' actual names and incorporates a story of something they may have told the teacher or class about. Another example specifically could be with mean, median, and mode, and using a real survey from the students in the class. This will engage students as they will want to figure out the class's answers and understand what mean, median, and mode mean for their class. Using real-world activities in lessons will also create great discourse that students will want to participate in. These real-world activities provide a sense of relevancy while also promotes group work and learning making math more fun and like a social activity.

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One strategy I would like to use in my classroom that promotes reasoning in Mathematics is teaching students to notice patterns. Choral counting specifically stood out to me. Choral counting is great for building math reasoning because it helps kids notice number patterns and understand sequences better. When we count together, they start to see how numbers build on each other, like noticing increments and connections. For example, counting by multiples helps them see links to the multiplication table or spot place value patterns. This way, they're not just saying numbers—they’re seeing how numbers relate and fit together.

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One possible teaching strategy that was mentioned in the text is choral counting. Teachers can implement this in the classroom by having students count in a structured format. I have seen this during my math observation with the teacher having students counts by ones, fives, and tens up to 30. This allows students to build connections between numbers and their relationships, as well as an understanding of how to count by different numbers. This can be utilized for many things, such as time, money, sorting, and counting collections. Having students practice recognizing patterns by choral counting can be used to help identify reasoning behind counting with patterns.

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A teaching strategy that can be used in the classroom to foster mathematical reasoning is discussion among the class. Discussion can be used in many ways in the classroom. The first is a class-based discussion. As a teacher, you can ask questions to the class to have them share their reasoning behind their work. Another way is to use think, pair and share in the classroom. This can be done randomly or with their neighbors. Ultimately, discussion in the classroom lets students explain their reasoning. This not only allows children to strengthen their understanding of a topic but is allows students who do not understand to see different tactics for solving a problem.

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One teaching strategy that can be used to promote mathematical reasoning in students is think-pair-share. These type of activities have many benefits. First of all, they allow a set time for students to think and strategize on their own. This helps build problem solving skills. Then when the student is paired with another, not only is it an opportunity to make a friend, but also to see how their classmate is solving the problem. Sometimes seeing different strategies is helpful for the student because they learn a new way that might work better for them. It also helps build the students confidence in their math abilities. By this I mean starting out by sharing to just one classmate, and slowly building the confidence to share to a larger group. After the think-pair-share, the teacher can ask if any of the pairings want to share how they solved the problem.

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Something that I did growing up that I thought was cool and something fun was getting to be able to work with a partner on a math problem and then being able to teach the other students in class. I think there are alot of benefits of this students are able to collaborate with others, they also then get to explain there reasoning to the whole class, and then the whole class gets to learn something as well.

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One teaching strategy to use in a classroom is to use manipulatives. Incorporating objects from student's real lives may engage them in their learning, especially when they supply the manipulatives. It engages their learning because they feel pride in participating in their learning. We have already discussed a way for this to happen in the classroom which is counting collections, but there are many other ways that objects from the outside world can be incorporated in a classroom.

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One teaching strategy that can be used to promote mathematical reasoning is using real-world problems. By doing this, it allows students to be able to connect math to things that are relevant to their culture. If students feel that they resonate to what they are learning and working on it will allow them to solve problems and be more engaged while doing so. As the teacher, this can look like modifying tasks so that the problem solving directly reflects what students are experiencing in the real world. It could also be creating an experience with pictures or videos to give the problem solving more meaning and encourage students to ask more questions that would support mathematical reasoning. Another way teachers could promote mathematical reasoning is by making problems more relatable by making them more personal, asking them to examine their own lives. This also plays into how teachers word math problems. If teachers are over scaffolding their questions it is stripping students of the opportunity to have to reason their work.l

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A teaching strategy that could be used to promote mathematical reasoning in the classroom is think-pair-share. This would looks like students discoving an idea for themselves, then finding a partner and collaborating on eachothers ideas. Finally, students can then share or present their findings. This could be used for a small discussion or could also be utilized when working on a big project.

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A teaching strategy to help students build mathematical reasoning is Think-Pair-Share with open-ended questions. First, students think on their own about a problem, like explaining why a solution works. Next, they talk with a partner to check and build on their ideas. Finally, they share their answers with the class, using questions like “How do we know this is true?” This strategy is important because it helps students explain their thinking, which makes their understanding of math stronger. By learning from each other and thinking carefully, students become more confident problem-solvers and develop important skills for the future.

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A teaching strategy that can promote mathematical reasoning is problem based learning. In this method, students work on a real problem that they need to solve using math. For example, they could plan a school picnic and figure out how much food and supplies they need while staying within a budget. Students would work in small groups to share ideas and discuss how to calculate costs. The teacher can help by asking questions like, “What math do we need to use?” or “How can we stick to our budget?” This way, students learn to think critically and see how math is used in their everyday life.

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Using real world problems is a great way for students to reason through their thinking. For example, a problem (Mrs. Smith has 15 pieces of candy and wants each student in a 30 student class to get a piece of candy how can she do this?) like this is much easier to understand then __ divided by __ equals 15. Students can see and understand a real world problem much easier then a simple math problem. Real world problems also get students more excited to do math and are more engaged throughout the problem solving process. The teacher can lead a class discussion through a real life scenario word problem. Asking different students for their problem solving strategies is a great way to get the whole classroom involved. Making the problem hands on (using actual pieces of candy in this example) would make the students even more engaged and excited to solve the problem.