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ijkijkevin – Multiple dimensions of teaching and learning. by Kevin HallMultiple dimensions of teaching and learning. by Kevin Hall
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How I’m Covering the Distributive Property in Precalc – ijkijkevin
https://ijkijkevin.wordpress.com/2013/09/11/how-im-covering-the-distributive-property-in-precalc/comment-page-1
Multiple dimensions of teaching and learning. by Kevin Hall. How I’m Covering the Distributive Property in Precalc. I teach a class called Math Analysis/Trigonometry, which is close enough to Precalc that students who get A’s in my class are allowed to skip to calc. I’m spending the first several class periods covering a combination of Carol Dweck mindset stuff and the idea of distributing. Distributing? In (x 2)/x , you can cancel out the x’s. With mistake #2, students mistakenly think that you can R...
ijkijkevin – Page 2 – Multiple dimensions of teaching and learning. by Kevin Hall
https://ijkijkevin.wordpress.com/page/2
Multiple dimensions of teaching and learning. by Kevin Hall. Dan’s “Shipping Routes” and Cognitive Load. During Dan’s series of lesson makeovers last summer, I intended to write up a critique of the Least Common Multiple makeover. Bringing up the issue of cognition, working memory, and inquiry vs. direct instruction again. So here are my thoughts. For context, Shipping Routes shows students the clip below and asks whether the two boats will ever get back to port at the same time:. Here’s how the st...
Genuinely differentiated grading with Khan Academy – ijkijkevin
https://ijkijkevin.wordpress.com/2016/10/08/genuinely-differentiated-grading-with-khan-academy
Multiple dimensions of teaching and learning. by Kevin Hall. Genuinely differentiated grading with Khan Academy. I hope this is my last post on Khan Academy for a while. It’s not that central to my teaching (I’d rather be writing about Desmos or something). But I do think the tool I’ve designed to differentiate grading with Khan Academy may be useful to some folks out there. But different students need to be held to different standards of retention and accuracy, per IEP’s and observations. On the opposit...
Creating Intellectual Need for Multiplying Binomials – ijkijkevin
https://ijkijkevin.wordpress.com/2016/03/24/creating-intellectual-need-for-multiplying-binomials
Multiple dimensions of teaching and learning. by Kevin Hall. Creating Intellectual Need for Multiplying Binomials. I’ve always needed a way to motivate the study of quadratics. In the past, I’ve used materials from some of Dan Meyer’s 3-Acts: Super Mario. To get students to realize that linear predictions are sometimes wrong, and Will It Hit the Hoop? I’d like to share a new lesson that I really liked because it:. Naturally focuses students on area models of quadratic expressions;. The most direct way to...
Burn the computer: personalized assessment on paper – ijkijkevin
https://ijkijkevin.wordpress.com/2016/10/21/burn-the-computer-personalized-practice-or-assessment-on-paper/comment-page-1
Multiple dimensions of teaching and learning. by Kevin Hall. Burn the computer: personalized assessment on paper. How can I adaptively target content to students’ needs without restricting assessment items to the lame formats — like multiple choice — that computers are able to read? Dan Meyer has chronicled those drawbacks in many blog posts, for example, this one. I like the way commenter Dan Anderson. Summed up the limitations of letting a computer assess student work:. And yet computers do have an adv...
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8. “We’re taking it away from one side and putting it on the other.” – Teaching With Problems
https://problemproblems.wordpress.com/2015/08/14/8-were-taking-it-away-from-one-side-and-putting-it-on-the-other
Essay on Cognitive Load Theory. My First Blog (2010-2015). 8 “We’re taking it away from one side and putting it on the other.”. August 14, 2015. In the video above, the student describes adding 4 to both sides as “taking the 4 away from one side and putting it on the other.” This is difference then “balance reasoning” or using the subtraction property of equations. Where does this “Give and Take” model come from? The “give and take” model is a way of seeing equation-moves. It helps make s...Maybe not....
1. How do kids think about solving equations? – Teaching With Problems
https://problemproblems.wordpress.com/2015/08/04/1-how-do-kids-think-about-solving-equations
Essay on Cognitive Load Theory. My First Blog (2010-2015). 1 How do kids think about solving equations? August 4, 2015. I want to get ready for the school year. I’ll be teaching Algebra 1, and that’s where solving equations happens. These skills are seriously useful, so I want to do right by my students. I want to teach this topic well. Actually, there are a few different ways of wording this question I might focus on. How do kids think about solving equation problems? I think I’m interested in ans...
Khan Academy Mastery Mechanics | Matt Faus
http://mattfaus.com/2014/07/khan-academy-mastery-mechanics
Skip to primary content. Skip to secondary content. Khan Academy Mastery Mechanics. July 3, 2014. If you’ve used Khan Academy, I’m sure you’re familiar with this graphic. It is shown at the end of each task to inform you of how you have progressed. You may not be familiar with the (somewhat complex) mechanics behind how students progress through each level of mastery, and that’s what I hope to clarify. First, let’s outline some vocabulary. Khan Academy has many different exercises. There are three ways s...
August 2015 – Teaching With Problems
https://problemproblems.wordpress.com/2015/08
Essay on Cognitive Load Theory. My First Blog (2010-2015). 9 How do kids think about solving equations? August 20, 2015. The last 8 posts in this series have been about working through different aspects of how kids might think about solving linear equations. In this post I want to try to synthesize what I now know about all this and ask some questions that I don’t yet know the answers to. In the previous posts, I looked at problem types that differed along the structure of the equation:. Ax b = cx d.
7. How kids might think about different types of equations – Teaching With Problems
https://problemproblems.wordpress.com/2015/08/10/7-how-kids-might-think-about-different-types-of-equations
Essay on Cognitive Load Theory. My First Blog (2010-2015). 7 How kids might think about different types of equations. August 10, 2015. I think what is really becoming clear to me is that the real work I have to do is in clarifying how kids can make sense of equations that go beyond the simplest cases. The simplest cases are ax b = c. And ax b = cx d. Things get more complex with equations of the type c x (ax b) = d. B – ax = c. I don’t know whether it’s worth it to identify b- ax = c /- dx. Though, come ...
3. How do kids think about “pick a number” problems? – Teaching With Problems
https://problemproblems.wordpress.com/2015/08/05/3-how-do-kids-think-about-pick-a-number-problems
Essay on Cognitive Load Theory. My First Blog (2010-2015). 3 How do kids think about “pick a number” problems? August 5, 2015. August 5, 2015. Source: http:/ algebra.mrmeyer.com/. I want to help students move from guess-and-check to using equality properties in the equation work. There are some problems that might be helpful in this work — like balance problems. What other problems might be helpful? 8220;Closed number tricks”? I’d like to get precise about what makes pick a number problems promisin...
6. Equation Strings – Teaching With Problems
https://problemproblems.wordpress.com/2015/08/10/6-equation-strings/comment-page-1
Essay on Cognitive Load Theory. My First Blog (2010-2015). August 10, 2015. August 10, 2015. From http:/ numberstrings.com/2015/01/30/true-or-false-can-a-number-string-develop-relational-thinking/. Other people talk about number strings. Whatever you call them, these are helpful for my arithmetic teaching for three reasons:. Students are likely to come up with different strategies for these problems, and this gives students a chance to contrast other strategies with their own. I think this helps kids...
About – Teaching With Problems
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Essay on Cognitive Load Theory. My First Blog (2010-2015). This is Michael Pershan’s blog about teaching. It’s my second blog (check out the links above). If you want to know what I was thinking when I started the blog, check the crossed-out text below. This blog represents my (i.e. Michael Pershan. 8216;s) project to improve my teaching and understanding of problem solving. The project, as I’m formulating it at the start (these things always change) involves three related questions. You are commenting u...
2. How do kids think about balance problems? – Teaching With Problems
https://problemproblems.wordpress.com/2015/08/04/2-how-do-kids-think-about-balance-problems
Essay on Cognitive Load Theory. My First Blog (2010-2015). 2 How do kids think about balance problems? August 4, 2015. August 5, 2015. When I teach students to solve linear equations, I’m aiming to help move them from guess-and-check to using the properties of equality. I’m in search of the ways of thinking that could help students move towards the more sophisticated techniques. Balance problems (i.e. mobile problems. And, in fact, there is a special way of thinking that balance problems allow for. I...
July 2015 – Teaching With Problems
https://problemproblems.wordpress.com/2015/07
Essay on Cognitive Load Theory. My First Blog (2010-2015). Thinking Through “Falling Leaves”. July 14, 2015. July 14, 2015. How will kids think about this? As part of the Math Forum’s EnCoMPASS project ( http:/ mathforum.org/encompass/. I sorted through and categorized about two hundred student responses to this problem. Here’s the thinking that I saw, with sample responses that seemed typical of the things that I saw. To recognize explicit functions to describe exponential patterns. This sort of analysi...
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ijkijkevin – Multiple dimensions of teaching and learning. by Kevin Hall
Multiple dimensions of teaching and learning. by Kevin Hall. Teaching linear functions for meaning. For years I’ve been rearranging the pieces of my linear functions unit like a jigsaw puzzle, trying to optimize comprehension for weaker students. Weaker students see math as a giant bag of disconnected steps to memorize, right? And even if you can give them an. Here’s a screenshot of the key question type I’ve developed to make that happen:. Here’s what I love about this question type:. This question impo...
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