Middle School Math Moments (now Cognitive Cardio Math)

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 3 - Examples of Differentiated Planning for Achievable Challenge   I took notes on this chapter last week, on a bus ride to NYC (to see Aladdin !), but it has taken me until today to actually write this post:) As the title of the chapter suggests, the author offers examples of differentiated planning and activities. In each example, students are learning the same basic concepts, but at different levels of challenge, which should lead to their maximum success and should minimize their frustration. There are several different examples, so I'll highlight a few in this post and the next. The first activity, which involves working with shapes, is called "Draw My Shape," which the author says is a good activity for Map Readers. The steps for the activity are as follows: 1) pair student that have similar abilities in shape recognition and in naming shapes, OR pair a high mastery/low communication student with high communication/low mastery student 2) give eac...

Chapter 2 - Understanding and Planning Achievable Challenge Differentiating instruction is the key to creating   achievable challenges for students, through instruction, homework, multimedia support, etc. In order to differentiate instruction, students' learning strengths must be understood, and Willis shares two general categories for students: Map Readers and Explorers. According to Willis, Map Readers like to work independently, and are most comfortable when they have specific instructions or procedures to follow. Map Readers have characteristics of the linguistic and logical-mathematical intelligence groups proposed by Gardner (1983), as well as learning styles of auditory, sequential, and analytic learners. They prefer problems with definite answers and procedures, they prefer new skills to be modeled by the teacher, process information in “parts-to-whole,” are comfortable with logical, orderly, structured approaches, and are good at using words to understand informa...

Chapter 2 - Understanding and Planning Achievable Challenge Willis begins the chapter by offering a few examples to demonstrate the frustration or boredom one might feel if not given an achievable challenge. One example – “you are dropped off at the top of a ski resort’s steepest run when you’ve only had experience on the beginner slopes OR you have to spend your day on the bunny hill when you’re an expert skier.” She relates these examples to the students who either do not have the foundational background to understand new topics in class or to those who have already mastered the current concepts. To be engaged, students need relevant, achievable challenges which are difficult enough to hold their interest and make them exert mental effort, but do not cause them to be frustrated. According to Willis, achievable challenge is powerful, because each success leads to increased levels of dopamine in the brain, which is accompanied by a sense of pleasure and decreased anxiety in re...

As mentioned in the first post about Chapter 1 , the author believes that students need to feel less stress and anxiety in order to be able to learn, so she suggests a few ways with which to reduce that stress. 1) "Retest to De-stress" Willis recommends offering the opportunity to retest, especially since math is based on foundational knowledge that must be mastered. She states that "mastery forms the basis from which students can extend their neural networks of patterns and concepts before they move to the next level." Retests provide the chance to reevaluate answers and make corrections. Willis states that she requires students to retest when they score under 85%. To address the concern that retesting permits students to be more irresponsible when preparing for a test (knowing they can retest), Willis states that there should be some accountability, such as requiring students to provide evidence that they have prepared for retests – like participating in t...

Chapter 1: Reversing Math Negativity with an Attitude Makeover Chapter 1 was a little hard for me to get through   - I don’t know yet if it’s the author’s style, my lack of time to read for an extended period and really get into it, or the fact that I’m reading it on a Kindle (I’m not a huge fan of the Kindle…I really like books with pages that I can turn, but I’m trying to use the Kindle). Anyway for whatever reason, it’s been slow-going for me so far :) Chapter 1 had a few points that I thought were very interesting, so I will highlights those as briefly as I can (the most interesting point to me is close to the end of the post, so I hope you read to the end...or skip to the end)!     In Chapter 1, Willis states that the first step to success in math is having a positive attitude, though many of our students don’t have one.   Willis discusses the idea that “being bad” at math, or disliking math, generally seems to be acceptable in our society. She c...

Do your students love math? Do some of your students hate math? I know that I always start the year with at least a few students who say they hate math. When asked why, they can't always give a reason, they just "hate it." Why is this, and what can we do to change this for those students that are more difficult to reach? While browsing on Amazon, I came across the title Learning to Love Math: Teaching Strategies That Change Student Attitudes and Get Results by Judy Willis, MD, so I decided to purchase it and see what the author has to offer. The book was published in 2010, but I hadn't seen it before...perhaps you have? In the introduction, Willis points out that the work force has an increasing need for people who have mathematical skills to solve problems (a higher-order thinking skill that is a function of the prefrontal cortex). The prefrontal cortex is also responsible for: personal responsibility, emotional response control, planning, prioritizing, g...