I say ever-dreaded because while Algebra Tiles have long been touted as an amazing resource, it's never been obvious to me how to use them.
If you haven't seen or used them, they are a collection of small squares that represent units, large squares that represent x^2, and rectangles (with a length that matches the large square, and a width that matches the small square) that represent "x." Students can use various combinations of the shapes to model equations and algebraic thinking, leading up to more formal mathematical processes.
I'm changing my mind...
- For students demonstrating slower processing speeds, manipulatives force the pace of learning to better match that of the student.
- They provide a means for students with working memory needs to better keep track of what they are doing, by displaying the process on the table in front of them.
- They allow students to make use of perceptual reasoning skills to accommodate for needs in mathematical computation.
This is something I need to start doing more of.This isn't an easy transition for me - building manipulatives into my arsenal of teaching tools is going to take a lot of learning (and playing?) before I'll be comfortable with them. But for now, I can at least envision what this might look like. When I go back to the classroom, I'll be aiming to:
- Physically move the manipulatives INTO my classroom (out of storage) and have them in an easily-accessible spot for everyone to get to, not out of sight in an office or tucked away in a classroom closet.
- Incorporate manipulatives purposefully into lessons - carefully choose which manipulative the students will be using and know why I'm choosing to use it. What process does it demonstrate? In what way will it help my students think/reason?
- Make manipulatives integral to the lesson itself, not just have it as an add-on to what we're learning.
- Challenge the students to whom math comes easily to use the manipulatives, and get them thinking outside of the memorization box. I hope this might also reduce the stigma of using manipulatives.
But I still wonder...
- How well do digital manipulatives benefit students (if at all)? Are apps worth investigating?
- What resources are available for getting good, challenging-yet-accessible activities with manipulatives at the secondary school level?
- How do students learn which manipulative to use when presented with a selection (or when they can choose what to use on standardized tests)?
- How can I best incorporate manipulatives into flipped lessons?
I'd love to hear of good resources already in use out there for activities and materials that actively engage high school students in learning algebraic processes, and try my hand at some of them!