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Strategies: What to Do When They’Re Stuck Jennifer Georgia 2020 LDSHE h o m e e d u c a t i o n c o n f e r e n c e Strategies: What To Do When They’re Stuck Jennifer Georgia Solid math understanding is made of a wide and deep knowledge base, flexible thinking skills, and a positive “can-do” attitude. These three components cycle over and over through the years, adding layer upon layer of understanding. If there are malfunctions in any of the areas, it will affect the others. Best-Practice Math Repair 1. Mitigate anxiety and promote positive emotions Common Math Malfunctions 2. Take multiple breaks, or have learning time 1. Math anxiety when the brain is calm (after dinner) 2. Attention problems: environmental or 3. Manipulatives! physiological 4. Multisensory learning, find patterns, create their 3. Weak number sense own math book, constant review through games 4. Weak memory 5. Roll back the thinking from abstract to mental 5. Inability to hold two concepts in the mind at image, to concrete, then to “vibrant concrete” once—fractions 6. Anything that promotes the development of 6. Inability to generalize—algebra inductive reasoning, or that gets kids out of math “ruts” (or even better, never lets them fall in) Decrease Negative and Boost Positive Emotions: Only attempt math when child is well rested, well fed, and has just had some movement time. Use eye contact, breathing, touch, and music to re-center and calm an anxious child. Use a timer: “How long do you think you should puzzle over this one before moving on?” Also keep the total math session fairly short—avoid the frustration/tiredness wall. Praise effort, not results. Bring on the zing! (games, math storybooks, videos) Occasional rewards also increase the happiness-quotient (don’t become overly reliant on them—they should be a pleasant surprise, not an expectation). Try to squelch negative talk about math--it poisons the brain. Use positive language, and show interest yourself. Show them how you use math in everyday life, and also you may want to watch videos or read books on fascinating math topics (see resources). Reduce the complexity of the entire process-- the skill sets in demand at the moment--by sometimes being the problem reader, sometimes the scribe, sometimes the “organizer.” Vary which task you perform so your child has opportunities to do each of them in turn. All of this will help her chunk a problem into smaller more manageable pieces and eventually be able to perform all the pieces. Let the child transition away from manipulatives naturally, when he can calculate more quickly without them than with them. Make sure he always has plenty of resources to turn to if he’s confused—then the anxiety brought on by the confusion can be channeled into a positive experience. With older kids, TRY to check in with them each day as they begin their math, to talk about what they did the day before, give some quick pointers if necessary, and a pat on the back. Even if kids are fairly self-sufficient, some attention feels good. Improve Cognition: Concrete <> Mental Image (Representational) <> Abstract As described by Jean Piaget, children begin developing number and operation sense best through modeling in the real world: math manipulatives. This should gradually build up in their minds images of the manipulatives that they can use to do mental math. Eventually, images are transformed to abstract ideas useful in higher math. When kids are struggling with math at a higher level, have them go backwards from abstract thinking to mental image, from mental image to using concrete objects. “How would you do this with apples?” If necessary, up your game to “vibrant concrete:” Wake up the brain by using more of the five senses (chocolate chips as counters), putting her name and her favorite things in a math story problem, going in the kitchen and use the measuring cups when thinking about fractions, using a toy car and track when solving distance problems, etc. “In our concern about the memorization of math facts or solving problems, we must not forget that the root of mathematical study is the creation of mental pictures in the imagination and manipulating those images and relationships using the power of reason and logic.” educator Mindy Holte 2020 LDSHE Home Education Conference (East) Strategies: What To Do When They’re Stuck — Jennifer Georgia (cont'd) Teach and model: Finding patterns in number sequences and charts; using the idea of simplifying a number sentence, rather than solving a problem; talking through a difficulty; drawing a picture or building a model; persistence and seeking resources to help. Help your child gain flexibility with his thinking by not hyper-focusing on “the one true way” of doing arithmetic—teach multiple methods and do lots of mental math. This should help when algebra time comes around. "Students are often given the impression that there is only one way to do a math problems, that math is rigid and inflexible. We need to instead look for opportunities to show that there are multiple ways to solve a problem, and elicit from our students their different ideas when we're doing a calculation or solving a problem…. Imagination is the ground from which knowledge springs." Jamie York Making Math Meaningful Solidify Knowledge: Build estimating skills, which lay a foundation for checking to see if their answer to a problem “makes sense.” Explore math facts with manipulatives, games, and real-world experiences. THEN memorize. Here’s our sequence: • Odds and evens • Skip counting by 2s, rhythm counting by 3s (stomp, stomp, clap 1,2, THREE, 4, 5, SIX…) • “Ten Pairs” • Doubles • Counting by 5s and 10s • Square numbers • Learn the 3 and 4 “chains.” For 3’s we like the song from the Schoolhouse Rock video. For 4s we sing it to the tune of “Jingle Bells.” • Learn several of the 9s multiplications tricks • Finish memorizing the other six multiplication facts: 4 x 6,4 x 7, and 4 x 8 (relate 4 x 8 to half of 8 x 8) Then memorize 6 x 7, 6 x 8, and 7 x 8 (5 6 = 7x8). That’s it, you’ve got them all! Now review with games and speed drills (for fun and profit). Addition, subtraction, multiplication and division all stand on the shoulders of these facts: 8+7= break 7 into a 2 and a 5 because you know your “ten pairs” and know 8+2=10, then add the 5. 6x13 = 6x10 + 6x3 = 78 Memorization of higher math skills and knowledge is less cut-and-dried, though some memorization can be helpful, especially when cognitive skills are weak. Things like order of operations, vocabulary for geometry and measurements, and some algebra rules should be memorized after being understood. Keep a notebook of all the math rules you find useful—to jog a rusty memory. 2020 LDSHE Home Education Conference (East) Strategies: What To Do When They’re Stuck — Jennifer Georgia (cont'd) Dyscalculia – Around 5 to 8% of otherwise “normal” people have severe math dysfunction. This can affect cognition and/or knowledge retention—development of math anxiety in conjunction with dyscalculia is common as well. They will likely struggle with this their entire lives, and need very explicit training, e.g. identifying key words in story problems to determine which procedures to use. May need professional help-- see this website: https://www.understood.org/en/school-learning/evaluations/evaluation-basics/understanding-evaluations Favorite resources for understanding math and math education Books: Lab Sheet Annotations and Mathematics for the Primary Teacher, by Lore Rasmussen This book goes along with the Miquon Math Lab course, but it has wonderful helps for anyone teaching math to children You CAN Teach Your Child Successfully, by Ruth Beechick Making Math Meaningful: Sourcebook for Teaching Grades 1 – 5 Math, …Middle School Math, …High School Math, by Jamie York et al. (He has some good YouTube videos also, along with online teacher training courses) The Joy of Mathematics and More Joy of Mathematics: Exploring Mathematics All Around You, by Theoni Pappas. Flatland: A Romance of Many Dimensions, by Edwin A. Abbott Flatterland: Like Flatland, Only More So, by Ian Stewart A Beginner’s Guide to Constructing the Universe: The Mathematical Archetypes of Nature, Art, and Science – A Voyage from 1 to 10, by Michael S.Schneider. How Not To Be Wrong, by Jordan Ellenberg Euclid’s Window: The Story of Geometry from Parallel Lines to Hyperspace, by Leonard Mlodinow What is Calculus About, by W.W. Sawyer The Psychology of Learning Mathematics, by Richard Skemp The Brain that Changes Itself, by Norman Doidge (a fascinating book on how brains are very flexible even into old age, but use caution—don’t hand this book to a teen interested in neurology—some graphic content) Video Resources for you and yours: 2020 LDSHE Home Education Conference (East) Strategies: What To Do When They’re Stuck — Jennifer Georgia (cont'd) YouTube: “Four Dimensional Maths: Things to See and Hear in the Fourth Dimension - with Matt Parker” TedEd math talks like “The Magic of Vedic Math” YouTube channels: Math Antics, Vi Hart, Numberphile, 3Blue1Brown, search for “Recreational Math” The Great Courses videos (we have them in our library, you can purchase or get a subscription): The Joy of Mathematics, The Secrets of Mental Math, Mathematics from the Visual World, The Joy of Thinking: The Beauty and Power of Classical Mathematical Ideas Khan Academy (of course) – check out the “Math for Fun and Glory” section Websites/Apps: MathIsFun.com, Wild.maths.org, Naturalmath.com, https://nrich.maths.org/11488 has many quick games to build up inductive reasoning skills.
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