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Memorizing Facts Versus Knowing Facts From Memory

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I used to think one of the most important things I did with my fourth graders was to make sure they were fluent with their multiplication and division facts.  My definition of fluency was synonymous with fast.  To me fast = fluent.  To ensure my students all had "fluency" with their multiplication and division facts, we had daily timed tests which some kids loved and others dreaded.  We used a boxed program that was on my self when I started teaching.   As much as I thought I was doing the right thing, there were a few things that bothered me about this process.  There were a few kids who were very proficient mathematicians who just were not doing well with these timed tests.  I also had some kids who were doing really well with the timed tests yet they were really struggling to multiply larger numbers.   After more and more of these concerns popped up over several years, I started doing some more research into what exactly fluency meant.  I ...

Math Workshop:Sharing & Reflection

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Welcome to the final week of our  Minds on Mathematics  book study.  If you missed them you can go back and read  Understanding Takes Time ,   Shallow Versus Deep Math ,  Starting Class  and Mini Lessons & Work Time .   This week are going to take a deeper look at ending class with sharing and reflecting when using a math workshop model.   Sharing Perhaps the most important part of a math workshop model is the time for students to share.  It is so important to stop work time before the end of your math class period and give kids a chance to share.  This is the part that helps to solidify their comprehension and gives them a chance to practice metacognition which is thinking about their own thinking.  They get a chance to synthesize their understanding, check on their progress and make goals for the next day.  Teachers can gather important formative assessment data about what strategies kids are using and where to go ne...

Math Workshop: Mini-Lessons and Worktime

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Welcome to week 4 of our  Minds on Mathematics  book study.  If you missed them you can go back and read  Understanding Takes Time  and  Shallow Versus Deep Math  or Starting Class .  This week are going to take a deeper look at the mini-lesson portion of math workshop and talk about what work time looks and sounds like.  Mini-Lessons Mini-lessons during math workshop should be - Short and focused (under 10 minutes) - Whole group instruction - Goal is fostering independence "The more I explained the less my students seemed to understand.  The more sample problems I did for them, the sleepier they appeared." (Hoffer page 103) This quote from the book perfectly sums up my past experience with teaching rather than listening . As I have shifted my practice from that of an expert giving out knowledge to that of a facilitator helping kids build their knowledge, this quote is no longer true.  Many of the ideas presented in this chapter wer...

Math Workshop: Starting Class

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Welcome to week 3 of our Minds on Mathematics book study.  If you missed them you can go back and read Understanding Takes Time and Shallow Versus Deep Math .   This week are going to look at how to start a day of math workshop. The Opening The first part of math workshop is the opening.  This is a time to invite learners to make connections and establish purpose.  The book outlines 4 parts to a successful math workshop opening. Welcome Learners If you are teaching a self contained classroom, this is your chance to make a transition to math class.   You might play a math song, check out a math you tube video , have kids share a favorite memory of math class or have some way to get kids pumped up that math is about to start.  If your students switch rooms for math and this is the first time you are seeing those students that day, this is your chance to greet kids at the door and work on making those connections with students.  It is your chance to wor...

Shallow Versus Deep Math

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Welcome to our second week of looking closely at math workshop.  Get more details about my math workshop book study here .   Deep Versus Shallow Math In this week's reading, I was struck by the difference between deep and shallow math.  Here are some characteristics of each type of math. Shallow Math - Memorizing algorithms - Applying an algorithm (usually a word problem found on the bottom of a page full of practice for that algorithm. - Hunt & copy exercises - Plug and chug numbers - Not considering what the numbers mean - About covering the content - Teacher gives out knowledge Deep Math - Engaging, exciting, exhausting & inspiring - Pushes learners out of their comfort zone - Mental models - An understanding of a concept that can be built upon later - Discourse - Challenging tasks - Students wrestling to make sense - Content understanding - Teacher as a facilitator of learning When I was in elementary and middle school 99% of the math I did would be classified...

Understanding Takes Time

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I know math workshop is for me!  Why?  Because I share these beliefs: 1) Students Are Capable of Brilliance 2) Understanding Takes Time 3) There is More Than One Way Welcome to part 1 of our Minds-On Math Workshop bookstudy .  Here are some of my thoughts from this week!  Students Are Capable of Brilliance      My best teaching friend and Kindergarten teacher extraordinaire has this as her mantra.  Her students constantly outperform other Kindergarten students in the district and she is always being asked to share her secret.  Her #1 reason her kids do so well is because she holds them to very high standards.  She truly believes that all kids can learn and in many ways their teacher's attitude about their learning becomes a self-fulfilling prophecy.  Her students learn because she believes they can.  ALL OF THEM.       Every time I feel like giving up on a kid and just "Teaching him how to do it" (aka arithm...

Why Don't We Get Math?

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     We are less than a week away from the launch of our new book study of Minds on Mathematics .  I had a few minutes today to dig into the book and wanted to share some of my thoughts about the introduction.   Why Don't We Get Math? -Cultural: It's Okay Not to Get It    This is the one I see the most in my school and in my life.  I see over and over again an acceptance among adults that math is hard and it is okay not to get it.  I know of several well educated adults who almost brag that their fifth grader does math they don't understand.  I have never heard a well educated adult bragging that they couldn't read at a fifth grade level.  As the author states, "this social acceptance of mathematical illiteracy is a huge barrier to our children's progress and preparation for life beyond our classrooms."  - Pedagogical: Math is Memorizing     When I was in elementary school math was all about memorizing.  The pare...