Darby Brenkman ETE 339

Double impact: Mathematics and executive function This article discusses  the goal of "double impact." This goal is to develop students mathematical proficiencies and executive  function skills at the same time. Executive function skills allow children to consider and change their own thinking. These are extremely important skills for children to have. The three categories of executive  function skills are inhibitory control, working memory, and attention shifting and cognitive flexibility. Inhibitory control is the idea that students need to stop to think about what they are doing before they instinctively solve a problem (possibly in the wrong way). Working memory means thats students have the capability to hold and process information they have read or learned. Cognitive flexibility is the capability of students to adjust their thinking and strategies to certain situations. All of these things can be adjusted or scaffolded to meet the levels and need...

Chapter 9: Supporting Productive Struggle in Learning Mathematics Summary: Students learn through productive struggle. Students learn to become problem solvers when working through struggles on their own. When students learn things on their own, they may find a bigger connection to it. Productive struggle does not mean that teachers allow students to struggle endlessly without support. Teacher should support students to learn and problem solve through their struggle. Teachers may ask questions to guide or redirect students in their learning.  Implications for Future Teaching: It is important that students learn how to explore academic concepts and learn rather than explicitly being told everything. I want to ask questions that help my students explore concepts and solve problems.  2 Questions: 1. How long should teachers let students struggle before stepping in? 2. Are there any other resources that teachers can use to guide students through productive str...

TA Chapter 8: Elicit and Use Evidence of Student Thinking Summary: It is important to consider how students think when planning, instructing, and assessing. Teachers can see what their students are learning based on evidence from their work samples. When creating lessons and learning tasks, it is important to envision what answers students might give. It is important to consider the ways their thinking may go. This will help teachers be effective in the classroom. Teachers need to interpret student thinking. This is the process of students taking student work and gathering the students' understanding from it. It is important that teachers build their following lessons based on what their students were thinking in previous lessons. Writing is a great way to pull students ideas out of them. Implications for Future Teaching: It is important that I use my students' knowledge and ideas to plan following lessons. I want to make sure I adjust my lessons to my students needs ra...

TA Chapters 6 & 7 Chapter 6: Use and Connect Mathematical Representations Chapter 7: Facilitate Meaningful Mathematical Discourse Summary: Chapter 6 discusses the importance of using representations such as manipulatives and drawings to model mathematical concepts. These visual tools can help students better understand what they are doing before they start solving problems more abstractly. Chapter 7 discusses the importance of the methods of teaching mathematics. One of the major discourses discussed was discussions whether these are whole class, small group, or partner discussions. Discussing concepts can help students put their ideas into words leading to a better understanding of mathematics.  Implications for Future Teaching: One of the major things I got from these two chapters is the importance of variety in instruction. While models can really help visual learners, discussions can really help auditory learners. I want to make sure I am catering to the nee...

TA Chapters 4 & 5 Chapter 4: Build Procedural Fluency from Conceptual Understanding Chapter 5: Pose Purposeful Questions  Children need to develop a foundational understanding for mathematics. This foundation includes understanding of relationships and operations. This is important, because as students advance, these things will still always be there. Mathematics can increase in difficulty, but it still includes basic concepts. Asking questions is a major instructional tool that teachers use. Teachers ask questions to see what students already know and to expand on what they know. It is important that teachers consider the questions they are posing to students and how they will deepen the mathematical understanding of students. Implications for Future Teaching: It is important that I give students a baseline or foundation of mathematical understanding. Even in the lower grades, students will learn concepts that they will use in the rest of their mathematical learni...

NAEP Reflection about your learning based on your work on student work: During part one, I learned the importance of creating a clear rubric that can be used to score problems. The best rubrics are those that are simple and clear. It was interesting to see how students solved the problems and discuss how our group would score them. Deciding next steps for students was helpful and something that I will use as a teacher each day. Reflection about your learning based on other work presented from participating in the discussion: It was really interesting to see how other groups interpreted their rubrics. Some of the rubrics were more or less clear than others. It was also interesting to see how groups scored students and how the students in the audience agreed or disagreed. I think this just made it even more evident that grading rubrics need to be clear.  Reflection about your learning based on your work on student work feedback: Working on part two, I learned how to ...

Ch. 3: Implement Tasks that Promote Reasoning and Problem Solving  Summary: It is important that teachers create learning tasks that will lead their students to an understanding of the concepts. There are different levels of demand when it comes to learning tasks. There are lower-level demand and higher-level demand tasks. Lower level tasks include things such as reproducing facts or formulas. Higher level tasks are more complex and many times include multiple steps that lead to a deeper understanding. Implications for Future Teaching: It is important that I balance the tasks I give to my students. They need to be given a combination of low level and high level demand tasks. 2 Questions:  1. How do you know that your students are ready to move from low level to high level demand? 2. How can you scaffold higher level problems to make them doable for all level students?

Ch. 2: Establish Mathematical Goals to Focus Learning Summary: Learning goals are the foundation for instruction, activities, and guiding students. Teachers set goals for their students and base their teaching off reaching those goals. In order to establish and reach goals, teachers need to implement tasks that promote reasoning and problem solving. Problem solving is a skill that students must learn in order to reach content knowledge. Posing purposeful questions is also important. Teachers ask questions that guide students towards the learning goals. Conceptual understanding comes from practice. During practice, teachers need to support productive struggle. Students learn better when they work through the problems and questions posed to them at a deeper level than the surface. Students need to make connections to the content and form representations of it. It is also important to use evidence of student thinking when working towards goals. Teachers change their instruction and met...

Summary This chapter starts with an addition word problem from the story The Hungry Little Caterpillar. This example focuses on students "putting their thinking on paper." The teacher then asks the students to explain their ideas and chooses which student examples to present to the entire class. The text discusses the idea of "ambitious teaching." This is an idea that requires teachers to meet the needs of ALL students in their class. This can be done by establishing goals, promoting reasoning, promoting problem solving, using representations, using meaningful discourse, posing purposeful questions, building procedural fluency, supporting productive struggle, and using evidence of student thinking. The text also mentions that students now are being taught in a different way than we were. When I was in school, I was memorizing facts, formulas, and strategies. Now students are using more creative and visual ways to solve problems. Impact on Future Teaching  In...