EEU209 Week 2 Ticket-In

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Kutztown University Of Pennsylvania *

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209

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Mathematics

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Feb 20, 2024

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docx

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EEU 209: Math Foundations PreK-1 Ticket-In #1 Ch. 1: Setting a Vision for Learning and Ch. 2: Teaching Mathematics /Problem Solving NAME: Emma Stalsitz DATE: 01/29/2024 DIRECTIONS: Complete this Ticket-In. Pay attention to the underlined part in each question. This is the name of the section in the textbook to read that will help you complete the questions. Page numbers are also included. THE WHY: Completing a Ticket-In before coming to class will provide the student with some background information. If everything you hear in class is brand new, i.e., if it is the first time you hear the information, it will be challenging to determine what you truly understand and whether you have questions. By reading the assigned material(s) before class, you will be a “step ahead” and “in tune” with what we will be discussing in class. After the first one: Here’s how I want you to do it: Save this document as a Word document (.doc or .docx). Complete your responses directly on your saved document. Submit your saved document into the Assignment Folder for this week. 1. Ch. 1: UNDERSTANDING AND DOING MATH (pp. 2-5) “To understand and to do math” is demonstrated by implementing the five strands of mathematical proficiency . Name and explain briefly each of these strands. - Conceptual understanding: Strong connection of relationships between ideas - Procedural fluency: Choose and implement the right strategy with accuracy and efficiency - Strategic competence: Make sense of math problems and find a solution - Adaptive reasoning: Think logically, explain, and justify your ideas - Productive disposition: Understanding of the purpose of math WHAT DOES THIS MEAN IN THE CLASSROOM? (PUT THE ABOVE ANSWER FROM THE BOOK IN YOUR THOUGHTS. In the classroom, the five strands of mathematical proficiency can be used in many different ways. For conceptual understanding, I would use modeling and concept mapping to ensure that my students are creating those relationships with their ideas and math. For procedural fluency, I would use Challenge 24 to help with the flexibility of numbers and a peer coach/tutor to explain the how-to. For strategic competence, I would use strategy cards and think, pair, share for trading. For adaptive reasoning, I would use poster proofs and questioning to ensure that my students can justify their answers and truly understand what they’re doing. For productive disposition, I would use combinations like arts and math, literature and math, and puzzles in math to make sure my students know the reason for learning math. 2. Ch. 1: UNDERSTANDING AND DOING MATH (pp. 2-5) Building on these strands for professional proficiency, the Common Core Standards name eight Standards for Mathematical Practice. First, list these 8 mathematical practices. Then choose one of these practices and explain why you think it is important for you as a teacher to help your students develop this practice. - Make sense of problems and persevere in solving them. - Reason abstractly and quantitatively. - Construct viable arguments and critique the reasoning of others. - Model with mathematics. - Use appropriate tools strategically.

EEU 209: Math Foundations PreK-1 Ticket-In #1 Ch. 1: Setting a Vision for Learning and Ch. 2: Teaching Mathematics /Problem Solving - Attend to precision. - Look for and make use of structure. - Look for and express regularity in repeated reasoning. The mathematical practice that I think is important for me as a teacher is to attend to precision. This practice is all about making sure that your students can communicate their answers and reasoning effectively. I think that this practice is very important for my students to develop because they will be able to explain why they got their answers. In turn, they will be able to see their mistakes and change their work appropriately. Also, I can stress the importance of precision in graphs and charts. WHAT DOES THIS MEAN IN THE CLASSROOM? (PUT THE ABOVE ANSWER FROM THE BOOK IN YOUR THOUGHTS. In my classroom, I would use the eight mathematical practices to establish the fundamentals that all my students will need in every math class. Specifically, I would attend to precision by encouraging my students to communicate precisely to not only me but other people as well. I would be looking for them to use clear, mathematically accurate definitions and terminology when communicating, conveying their reasoning for a math problem, and so much more! 3. Ch. 1: HOW DO CHILDREN LEARN (pp. 5-6) and TEACHING FOR UNDERSTANDING (pp. 7-11) Explain what is meant by instrumental understanding ? Explain what is meant by relational understanding . Name the type of understanding you will strive for when you are teaching math to young children. Explain. Instrumental understanding is knowing a mathematical rule and being able to apply it. Relational understanding is knowing the appropriate way to solve problems using logical reasoning. When I am teaching math to young children, I will strive to teach relational understanding to my students. This understanding emphasizes forming a deeper understanding of mathematics. WHAT DOES THIS MEAN IN THE CLASSROOM? (PUT THE ABOVE ANSWER FROM THE BOOK IN YOUR THOUGHTS. In my classroom, I would use relational understanding. To implement this, I will focus on connecting ideas for my students and helping them build their understanding over time. 4. Ch. 2: TEACHING THROUGH PRPOBLEM-SOLVING: AN UPSIDE-DOWN APPROACH (pp. 14-16) For many years, math has been taught using the I/We/You approach and this approach has not been very successful in helping children understand mathematical concepts. Explain one of the reasons why this approach has been unsuccessful. One reason that the I/We/You approach has not been very successful is that it makes the student believe that there is only one way to solve a problem. This notion is incorrect since there are many ways to think about and solve every problem in mathematics.

EEU 209: Math Foundations PreK-1 Ticket-In #1 Ch. 1: Setting a Vision for Learning and Ch. 2: Teaching Mathematics /Problem Solving WHAT DOES THIS MEAN IN THE CLASSROOM? (PUT THE ABOVE ANSWER FROM THE BOOK IN YOUR THOUGHTS. In the classroom, this means that I will simply not use the I/We/You approach. Instead, I would focus on making sure that my students can explore various ways of thinking about and solving one problem. I think that this is a very important thing because every student learns and processes information differently so one way may work for some students but not others. 5. Ch. 2: ORCHESTRATING CLASSROOM DISCOURSE (pp. 24-29) The value of student talk during math lessons cannot be overemphasized. And there are ways for a teacher to encourage student talk. In your reading, 5 “teacher actions” for orchestrating productive math discussions were identified. These “teacher actions” are often referred to as “talk moves. Name and explain briefly each of these “talk moves”. Then, give an example (from your own educational experiences) in which a teacher demonstrated one of these “talk moves”. - Revoicing: Restating the statement as a question. - Rephrasing: Restate another’s ideas in their own words. - Reasoning: Ask what a student thinks of another’s ideas. - Elaborating: Students can give an example, share a connection, or add on. - Waiting: Using quiet time as thinking time. In my educational experience, I have had a lot of teachers rephrase. Specifically, my math teacher would always pick from a name jar and ask our opinion/answer/reasoning for a problem. After we gave our response, he would pick another name and ask that person what their idea was on the previous person’s response. This worked pretty well in my class and I can see how it promotes student talk during math lessons. WHAT DOES THIS MEAN IN THE CLASSROOM? (PUT THE ABOVE ANSWER FROM THE BOOK IN YOUR THOUGHTS. In the classroom, I will try out all of these “talk moves” and see which one works best for me. I understand the value of student talk and how it can drive a conversation a certain way/give the teachers cues about what their students need for review or time on. I’m interested to see which strategy works best. At the same time, I wonder if the strategy I use will differ from class to class.

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