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Found 3 results

  1. I just wanted a snazzy sounding title 🙂 In my experience, I have found that for many students fractions are the make-or-break concept for their mathematical literacy and competency in higher level mathematics and I've been working to build out my delivery and scaffolding of fractions. I have found that many students struggle with fractions because often fractions are the first topic in mathematics where context is as meaningful as the numbers and operations themselves. It can be very difficult to work through fraction problems without understanding what the symbols mean. There are a few things that make fractions seem complex to young students, such as: an incomplete understanding of the basic operations +, -, * and / can be uncovered when students begin to work with rational numbers and fractions. Because this is the first time that a student may be exposed to a more nuanced meaning of the operations, their confusion and thus struggle may mistakenly be attributed to rational numbers. the need to be mindful of context and thus unit-blindness the algorithms for calculating fractions can seem very random/arbitrary when you don't understand the operations or the meaning of fractions themselves (or both). an under-developed understanding of fractions and their various context-based interpretations. the widespread use of the notation a/b for different concepts. It doesn't matter what curriculum you use in your homeschool or tutoring. Fractions are a concept that many kids struggle with. In my own teaching, I've found that really developing strong unit-awareness while still working with whole-numbers greatly helps to ease the transition to fractions. Another practice that I've found helpful is getting students very familiar with numerical expressions. Anyway, I want to open the floor now to discussion of strategies for teaching the concepts with-in the fraction concept in such a way that students are not lead-in ever-widening circles of confusion and despair--which is how some kids really seem to feel when it comes to fractions. Most students want fractions to make sense, and when they feel as though fractions don't they can turn to the dark-occult practice of Algorithm Worship.
  2. What in basic school mathematics do you feel is "Need to Memorize" and why? What content, facts, patterns or relationships has your combined insight, experience and education led you to realize is truly useful for students to know as they continue through the continuum of mathematics. Memorized in this context simply means reliably committed to a memory that is easily and reliably accessed and activated when needed. I don't want to get super technical about what it means for something to be "memorized" in this context. Use your best judgement. It can be anything from the scope/sequence of school mathematics. You may quantify your response, such as "Before Grade_, kids benefit from having memorized..." or "To thrive in ____ topic, kids need to have..." One last thing, I know that this question invites a list-style response, but please take the time to explain why something made the list or what it is about it that leads you to feel that it should be memorized. Your justification could provide useful insight for someone else who reads this topic down the line. Please enjoy, 🙂
  3. So, the role that language plays in teaching arithmetic, particularly in primary/elementary school level, interests me a lot. It's something that I've been thinking about quite a bit for a while now. If you had to give each of the operations a simple, plain-English definition (or interpretation) to be used in 1st-8th grade arithmetic, what would it be? Please note the range there. If your definition is only good enough for a sub-set of that range, can you think of a way to improve it? (It's okay if the answer is "no") To be clear, the arithmetic operations are: Addition Subtraction Multiplication Division I'm especially hoping some of our Math-minded homeschooling parents will chime in on this, but everyone is invited to chime in. If you feel that you're elementary math series of choice gives a really good definition for the operations, please share the definitions/meanings that the series uses. (Hint: you may need to check the teachers guide to get the definitions/explanations as opposed to just the student text).
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