Darby Brenkman ETE 339

NCTM Illuminations Fraction Models url:  https://www.nctm.org/Classroom-Resources/Illuminations/Interactives/Fraction-Models/ Objectives, Concepts, Relationships Fraction Models is a tool that displays all the ways fractions can be expressed. It is a great way to explore fractions and develop a deeper understanding of them. It will show you a fraction as a fraction, a mixed number, a decimal, a percent, and visually in a portioned drawing. Students can manipulate the numerators and the denominators. This resource is for 6th-8th grade. The level of complexity of the fractions can be adjusted to match students level. Evaluation of App The app is very easy to manipulate. It is clear and visually appealing. Benefits/Challenges  This app is a great way to have students explore fractions and gain a deeper understanding of them. This app could also be translated easier to a reference/notes sheet to help struggling students. One thing I wish this app did was allow s...

"Sliding" Into an Equitable Lesson Summary              A kindergarten teacher planned a geometry lesson around Gutierrez's four dimensions of equity. The four dimensions of equity are achievement, access, identity, and power. Achievement is numerically and academically based. Access is implementing the concepts and having connections to the ideas. Identity includes the students backgrounds and the knowledge they bring to the classroom. Power makes students feel as if they are in the position to be doing what they are doing. For example, the teacher in this article referred to his students as mathematicians. The article discusses the value of students cultures, backgrounds, and ideas. When teaching with these dimensions, students will learn more than just mathematical concepts. They will learn problem solving, thinking, perseverance.              When planning the lesson, the teacher con...

GCI Chapters 10, 11, & 12 --> Ch. 10: Developing Classroom Practice: Engaging Students with Each Others Ideas This chapter discusses the levels of engagement in mathematics. The first level of engagement is comparing an idea to other ideas. Students should discuss their strategies and see how their strategies are similar or different from other students strategies. The second level of engagement is attending to detail in other students' strategies. This can allow students to get a deeper understanding of what exactly is being done to solve the problem. Lastly students should build on other students ideas to deeper their own understanding. Students should support the ideas of others and share their own. This can increase the amount of understanding for all students. --> Ch. 11: Mathematical Principles Underlying Children's Mathematics This chapter discusses the commutative, associative, and distributive properties. The relationship between subtraction and divis...

GCI Chapters 7-9 --> Chapter 7: Children's Strategies for Solving Multidigit Problems      Chapter 7 discusses strategies that children use when solving multidigit problems. When adding and subtracting, students can directly model with ones or tens. When modeling with tens, students are using their previous base ten knowledge. Students also invent algorithms to solve problems. When adding students add tens and then ones and then add them together. When subtracting, students subtract tens place and then remaining ones place. Algorithms can include incrementing, combining same units, or compensating. Allowing students to invent their own algorithms allows them to connect to what they are learning and often times avoid misconceptions.      When multiplying and dividing, students may directly model with tens, use addition strategies to multiply and divide, invent multiplication and division algorithms, and use base 10 strategies with manipulatives. --...

CCSSM Reflection  --> Evaluation of Project My group was assigned the second mathematical practice standard "reason abstractly and quantitatively." Our infographic and video define reasoning as how students make sense of things. We stated that reasoning can be implemented by reflecting on ideas, practicing, discussing, considering real world situation, and forming questions and hypotheses. We discussed the importance of student involvement and thinking and reflecting. We also discussed the process of developing number sense. I think my group did a nice job of discussing the importance of the standard as well as providing details and examples. --> Reflection on learning of the Standards of Mathematical Practices The Mathematical Practice Standards help teachers design lessons requiring students to think and reason about mathematical concepts. There are eight standards, but I think that they are all related, because they all have the common goal of mathematical pr...

--> Chapter 4: Multiplication and Division Problem Types and Children's Solution Strategies Multiplication and division problems are grouping and partioning problems. The unknown can be the amount of groups, the amount in each group, or the total. In multiplication problems, the total in unknown. In partitive division problems, the amount per group in unknown. In measurement division problems, the number of groups is unknown. Strategies for solving these problems include direct modeling, counting and adding strategies, and number fact. Number fact strategies involve numbers with common relationships. --> Chapter 5: Beginning to Use Cognitively Guided Instruction Cognitively guided instruction involves understanding how students think to solve problems. When using CGI it is important to engage children in the process of problem solving. Students have to be taught how to think as problem solvers. It is also important to consider what problems are being selected and their ...

--> Chapter 1: Children's Mathematical Thinking Children many times see mathematical problems in different ways than adults do. Children see math differently, but that does not mean they see it incorrectly. There are different types of addition and subtraction problems. Adults may see all of these problems the same, but children see them differently based on their structure. There are multiple strategies children use to solve these problems. With encouragement and engagement these different strategies come naturally to children. --> Chapter 2: Addition & Subtraction Problem Types Addition and subtraction problem types show/describe how children solve the problems. The different types are categorized based on the types of actions or relationships. Different structures present different levels of difficulty. The four types of addition and subtraction problems are join, separate, part-part-whole, and compare. There are also subcategories. These have different unknowns....