Association of Teachers of Mathematics in Maine

Chapter 6 Response Choice 2

09 Mar 2019 7:05 AM | Anonymous member (Administrator)

Think about the strategies you use to help learners make connections in their learning. What is the mix of near and far transfer opportunities (describe on page 177 & 178) you provide your students? How do you think about  introducing/scaffolding these opportunities for learners?

Comments

  • 09 Mar 2019 8:30 AM | Anonymous member
    With my enrichment groups, I focus both on near transfer and far transfer. I usually start class with a problem of the week based on a question from illustrative math, or from a competition practice question to help students activate prior learning. Sometimes, these questions are ones that review what students learned previously from me, sometimes I use the questions related to vocabulary to assess student understanding in context, and sometimes the problem of the week relates to the rest of the lesson. I would consider these questions near transfer experiences because the intent is that students would be able to replicate their thinking in a competition or testing setting. I also sometimes focus on a scenario where I ask students to construct meaning. One I recently did with my third graders asked students to use tiles to build different formations for a space station to determine with configuration would be better. In this case, better was using less tiles due to having to bring the pieces to space. They had certain criteria and constraints to follow, and they learned about making a table and patterns that included squaring a number in the context of the question. Later, students readily used the table, pattern, or a mixture of the two when doing a different problem-solving question. I didn't suggest this, they just asked for tiles or graph paper to help them model their thinking. The questions were not set out in the same way that the space scenario was which is an example of far transfer. When introducing/scaffolding opportunities for students I try to do think alouds as I'm first teaching the thinking of a new problem-solving strategy and model the strategy for my students, and then allow them to try modeling the strategy side-by-side with my younger students, or in a pair or group.
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  • 25 Mar 2019 10:28 PM | Anonymous member
    One of my goals this year has been to make connections to prior learning, as we approach new units. As I am just starting Geometry B again, I have started the Quadrilaterals Unit in the last week. Our Geometry A course discusses one dimensional midpoint and distance, which we now extend to the two dimensional coordinate plane. Reviewing and then comparing the formulas has added some incite for students.

    The slope formula is developed as an extension of rise over run, with height and width connections to one dimensional distance and incorporating the pythagorean theorem. I have used the Chutes and Ladders game in the past to have students note the patterns on the "board", positive vs negative slopes, and points as they would be in Quadrant 1.

    Firefighter Math:
    https://www.nwcg.gov/course/ffm/vert-horiz-and-slope

    This site has great "real-world" application to promote purpose to learning formulas.

    I sometimes have the time to help the students build quadrilaterals from different types of triangles (using reflections, rotations, and translations). For example, an obtuse scalene triangle can be reflected over the longest side to make a kite or rotated around the midpoint of the longest side to make a parallelogram. A scalene right triangle can be rotated around the midpoint of the hypotenuse to create a rectangle. An isosceles right triangle could be reflected (or rotated around the midpoint of the hypotenuse) to create a square. This help students develop the properties of quadrilaterals (relationships of the side lengths).

    Pam
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  • 27 Mar 2019 10:08 AM | Anonymous member
    I think connections are a key to students not only grasping, but maintaining understanding of material. In this world of proficiency and retakes, I have found that students are learning for the tests and then forgetting material like never before. BUT, if I can make the material relevant, their understanding goes way up. In Algebra 2, certain concepts like exponential growth and decay are great for student engagement, because I can take the concepts and apply them to things like bank accounts, sociology and population growth, or even make fun examples about zombies taking over the planet. Quadratics are great for carpentry, optimizing space with given constraints. Career and social applications, which I would put in the "far" transfer category, are great for encouraging students that the math really DOES matter.

    In terms of near transfer, I feel like that happens naturally every day. Working through operations with complex numbers is the same as working with polynomial operations. Factoring strategies pop up in quadratics, polynomials, rational functions, even up in to trigonometric functions and identities. Graph transformations follow all the same patterns. In my lessons, I find it extremely helpful to relate what we're talking about to problems of the past. When I teach polynomial division, I like to first work through the old school long division students saw in elementary school. If we're adding or subtracting rational expressions, it's nice to go back and talk about connections with common denominators, and least common multiples. Near transfer should really be happening every day as we build connections in the math classroom.
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