Middle School Math Moments (now Cognitive Cardio Math)

Chapter 1: The Nonnegotiables of Effective Differentiation I'm very excited to get started with this book; it's a great topic! So far, it's interesting and a pretty quick read. This is summary of the important ideas in the chapter....sometimes I get a little detailed, because I don't want to miss anything! In Chapter 1, the authors reinforce the idea that differentiated instruction is not new. (This was discussed in the intro ). Though students are in classrooms with others of the same age, students are not "the same." In spite of this, and because of all the material there is to cover, many teachers teach their students as if they are the same. According to research, students will engage more with learning and will learn more robustly when the learning is designed with students' differences (and similarities) in mind. A learner-centered model views the teacher's role as one that is responsible for covering material, but also one that is ...

It's summer-time and time to get some reading done! Myself and my Tools for Teaching Teens collaborators are going to read and review Differentiation and the Brain, How Neuroscience Supports the Learner-Friendly Classroom , by David A. Sousa and Carol Ann Tomlinson.We will each be reviewing different chapters, and those blog posts will be linked together as we go. If you're interested in learning more about this book, check back and follow the links to the different chapters:) I'm going to give a quick review of the book introduction here, and then later today I'll be reviewing Chapter 1. According to the authors, differentiation is brain-friendly and brain-compatible! They describe the rise, fall, and rise of differentiation, starting with the one-room schoolhouses, where teachers taught all subjects to all students, of all ages, and HAD to differentiate - there was no other way! As the country's population grew, public schools grew, and students were separat...

Chapter 3 - Examples of Differentiated Planning for Achievable Challenge This is a continuation of Chapter 3, from a couple of weeks ago (I had my notes written, but it has taken me a while to type them!!). In the previous Chapter 3 post , I reviewed a couple of the examples of differentiated planning and activities that the author offered. In each example, students are learning the same basic concepts, but at different levels of challenge, which should lead to maximum success and should minimize their frustration. This example is called Exploring Number Lines, and the author states that it is a helpful activity for both "explorers" and "map readers." As a preliminary activity, students explore number lines without any specific assignment; the author suggests using large number lines that can be rolled out on the floor. Students meet in groups and create KWL charts. In working with the number line, students will predict where they will end up with certai...

Chapter 10: Pulling It Together: Lessons, Anchors, and Tools In this chapter, the authors summarize how they have characterized differentiation in a math classroom: 1) Responsive teaching 2) Organized and flexible approach using a diverse collection of strategies 3) Purposeful adaptation of teaching and learning processes to accommodate the ways different students learn 4) All students have access to math knowledge and are appropriately supported and challenged 5) Teaching and learning in a problem-solving environment 6) Providing all students with opportunities to reach high standards, to reach their full potential, and to become proficient, independent learners in math. They have included a handy table of the lessons that were referenced in the book, along with the grade level and math strand addressed, so it's easy to go back and find any lessons you'd like to use. The authors address anchor activities again, review the idea that these are act...

Chapter 9: Teacher Knowledge of Mathematics and Pedagogy In order to teach for math proficiency, which is a driving reason for the differentiation discussed in this book, the authors state that the following National Research Council (2001, 2010) strands must be interwoven into a teacher’s practice: 1) Conceptual understanding of the core knowledge of math, students, and pedagogy 2) Procedural fluency with instructional routines 3) Strategic competence in planning and responding to problems 4) Adaptive reasoning in justifying, explaining, and reflecting on practice 5) A productive disposition toward math, teaching, learning, and improving one’s practice In chapter 9, the authors focused on the first and the last of these strands. In support of strand number 1, Carol Tomlinson (2001) is again referenced – she believes that gaps in a teacher’s understanding of   content is the most significant barrier to effective differentiated instruction. (Gaps in p...

This post has been moved to: http://www.cognitivecardiowithmsmm.com/differentiated-math-classroom/chapter-8

In the fourth lesson presented in Chapter 7, the differentiation is for readiness and learning styles. This fraction lesson, dealing with the concept of half, was designed for second grade. The class used tangram puzzles and triangle grid paper (duplicates of the small tangram triangles). The launch part of the lesson was a discussion of the tangram pieces and the goal of the lesson was shared: to show one half using the tangram pieces. An example, with discussion, was shared using the overhead projector. During the exploration , students worked individually, with their own tangram sets. The students’ task was to represent a tangram shape on the triangle grid paper, and shade in the halves of the shape using two different colors. They were then to cut their shapes out and glue them to a class poster. During the summary , students spent time digesting what was on the poster. Each student had to go to the poster, point to a shape that was showing one half, and expl...

The third lesson in this chapter addresses area of a circle and is differentiated for process, product, student interest and readiness. The lesson has a menu of seven activities to give students a variety of experiences in finding the area of a circle. Each menu item is a different strategy for determining an approximate area of a circle, with the objective being that students understand the concept of area of the circle as well as the formula. Students were paired with another student, based on interests, strengths, learning styles, personality, and readiness. All students completed menu item number 7, and then each partnership was assigned 2 other menu items. If they completed these, they could complete as many of the other items as they had time for. The menu items/strategies were: 1) Count squares 2) Inscribe and circumscribe squares 3) The octagonal/Egyptian strategy 4) The simulated parallelogram – Kepler’s derivation 5) Find area by weighing 6) Measuring area ...