Make math cognitively accessible with images and meaning filled
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Slides accompanying presentation at Faculty Summer Institute in May 2018.
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Make math cognitively accessible with images and meaning filled
- 1. Make Math Cognitively Accessible With Images and Meaning-filled Activities
- 2. Why make things visual?
- 6. Conversion 5 yd2= ____________ ft2 1 5yd 2 1 yd 3 ft 1 yd 3 ft
- 7. One square yard 1 yard 1 yard
- 8. One square yard (yd2)
- 12. https://mathvisuals.word press.com/ -- mostly basic arithmetic, but I use this for ideas.
- 21. One that I like -- “seeing divisibility.”
- 27. Number line “quick image”
- 28. GIMP
- 30. • https://youtu.be/9bMJH6aQwsw?t=44s “cut out an image using paths” • https://youtu.be/vzM4S3nEmqA You tube upload of “let’s make a line.” • Play
- 31. How to make it meaningful
- 32. Assume competence, but provide guidance. • Provide practice that includes retrieval from the mind, not the paper. • Require it. • Low-risk Assessments. • Structure Structure • https://www.chronicle.com/article/Traditional-Teaching- May/243339?cid=wsinglestory_hp_7 •
- 33. Reaching more students • https://Landmarkoutreach.org/blog-post/making-math-instruction- stickier/
- 34. Step One
- 39. Instructional Routines & Principles • Connecting Representations • Quick Images • Don’t mix confusing things until one of them is mastered
- 40. Exponents
Editor's Notes
- (ask and get responses … see if you can set this up so your mouse works like a pointsr… BUT break the chain of math not being meaningful …. Also mention that …. More students can understand – SWD and ELL… less language dependent …
- https://buildingmathematicians.wordpress.com/2016/07/12/some-thoughts-about-spatial-reasoning/
- (
- So,… how can we get studnets thinking like this? My students come with worksheet type problems like this, and yes, they tend to go to “what’s the procedure?” and we have a procedural way to address this, to wit: …. And this works reasonably well. However, many students ask why. This all makes a lot more sense if:
- Some of my students are very accustomed to surviving, not thinking, so I might mention this is measuring this whole 2-D space… “area, squarea” … which is why it’s called square yards…
- and then note that each of these guys is … a square foot. I’ve learned to give wait time on this. I had one student ask all kinds of questions about this… and then ask… “okay, that’s what the 2 above it means… what if … what if … we put a 3 up there? No, tell me about that tomorrow.” That student got the top grade in his math class that semester and has gone on to do well in the next two classes … and I’m reasonably sure it is because we didn’t hurry him up. How can we get them *thinking* like that, though? And… how can I not have to draw quite so many squares?
- Well, this is what my wall looks like. Students can – and do – get up and look at it.
- Another handy dandy viusual is this number line, which I’ve got in two places. For a lot of students, vertical makes more sense than horizontal at first – and it was easier to do in my room
- Geogebra is a free, open Java and HTML5 based program (online or downloaded to computer) providing interactive algebra, geometry, statistics, and calculus applications so students can see and do math. https://www.geogebra.org/materials shows resources ….. You’ll want to click on “show all.” This is open source and I’m not sure what gets an app up on the front page. There are half a dozen people who seem to be behind most of the materials, and they also do training workshops; we’ll have one out at Parkland in June and it’s almost full but if you’re interested, let me know. Scroll down for the tutorials – I have found the “classic” ones to be most useful b/c it’s not being changed. I’ll let you explore them …
- This is one of my favorites.
- Now, here’s the amazing and open thing about Geogebra. While I like this, … I would like to tweak it a little here and there. I can wander over and open this in the Geogebra App and click a few things here and there and…
- I can make my own copy and … do what I’d like with it. It’s not easy to figure out but that right hand column is the “construction protocol” that lists every step taken by the creator.The left column is showing the elements that were added, either by category or by the order added.
- But let’s nto get ahead of ourselves. Let’s just say I wanted to make my own visuals and images for my work. If you haven’t figured out yet, I’m kinda into “open” and I want to be able to share what I do – which means I have to own what I do. I’m going to first make my own star in Geogebra. Here’s how:
- Free, open source image editor. Much like Photoshop – but free. Also, not “free for the basic version…” it’s just plain free. It’s very powerful. It’s also got lots of tutorials.
- Make the google doc with all the links, dear one, including this one https://youtu.be/vzM4S3nEmqA
- Students don’t automatically make connections. In our Pre-Algebra course, students are allowed to use times tables charts. They are *not* allowed to use calculators for learning basic calculations. They learn to use the times tables sheets – and they are 25 by 25 – for multiplication and division. They use them a *lot.* If they don’t have number sense – and most don’t – they’re using them for easy ones …. They don’t pick up, even the ‘easy’ ones… they just keep looking t hem up and wearing the chart out. They can get to where they *do* have better number sense for “that answer is way too big…” But … that’s because we use the visuals as a bridge, not a crutch.
- https://www.chronicle.com/article/Traditional-Teaching-May/243339?cid=wsinglestory_hp_7
- Landmark School is a school for students with specific language learning disorders.
- Notice: there aren’t as many triangles.
- Encourage them to remember instead of copy… to try to recall w/o looking back at the notes. Learning about retrieval
- Classic example. How often do we just say and pray: DON’T MULTIPLY DON’T JUST MULTIPLY….. And we just teach with the symbols. Many of them are saying “five … three” Let’s make some videos about this, too. We can do a lot in a minute or two. Insert video here!
- Much of the emphasis on “developmental education” and math is on accelerating, but even the proponents of the acceleration acknowledge say that their ideas could work for “as many as half” of students who place in developmental courses. (https://www.insidehighered.com/sites/default/server_files/files/CCA%20Remediation%20ES%20FINAL.pdf, p. 5 ) Other research where instructors are interviewed include their acknowledgement that many students don’t benefit from acceleration, but from building missing foundations. For example, this article* compares the effectiveness of rules-based vs. conceptual instruction. Spoiler: Conceptual wins (see also https://www.carnegiefoundation.org/wp-content/uploads/2013/05/stigler_dev-math.pdf ) I provide academic support for students in our most basic math courses. Many have learning disabilities (my area of expertise); many believe that they “can’t do math.” We have excellent teachers and materials (mostly not OER), who teach concepts and provide reinforcement and support (such as my tutoring), so I have seen that it’s possible to change minds and results. How can that be scaled up? I believe that the OER community can and should collaborate to create resources to improve the cognitive accessibility of math, and facilitate professional development for effectively using them. THere are some very good resources already– a quick search at oercommons.org yields 249 results. Many are individual lessons (some excellent ones from Designers for Learning** service learning course, which I participated in) but there are also full courses with conceptual frameworks. I’m also participating in a “Power In Numbers” project where we have curated lessons and will be “creating OER curriculum” — but small scale curriculum; we commit to a few hours per week for not so very many weeks. The focus on this project is “advanced” math, too (algebra and above). However, many widely used adult basic education math resources are accelerated repetition of procedural instruction, and when that proves ineffective, the student is often deemed “not able.” From the “Bridge to Nowhere” article: “And those who seek to attend a community college with what amounts to little more than a basic understanding of fractions and decimals should be encouraged to enroll in high-quality career certificate programs that embed extra help in the context of each course and lead to jobs that pay well.” It fails to provide any examples of these programs. I don’t wonder why. I think the OER community can create and disseminate interactive, multisensory OER to open doors of opportunity, whether for those “high quality career certificate programs” or already established adult education. Whether it’s lessons using manipulatives (especially in rural areas or correctional institutions where internet access is limited) or interactive OER at sites such as geogebra.org , there is so much potential for reaching the adult basic education community. That said, it requires that community. How can we make this happen? *You’ve Got to Learn the Rules”: A Classroom-Level Look at Low Pass Rates in Developmental Math. By: Cox, Rebecca D., Community College Review, 00915521, Jul2015, Vol. 43, Issue 3 **https://designersforlearning.org/