* Informal Geometry Explorations from Dale Seymour Publications is a treasure trove of geometry puzzles. Through hands-on activities they encourage students to develop inductive reasoning and great geometric vocabulary.
What I liked about it: I would totally use this in my class to jump start (or to verify understanding of) a topic!! Some of them are just fun thinking-outside-of-the-box activities that build spatial awareness, but many of them require working knowledge of geometric vocabulary as well. The activities vary in the amount of intuition required, so you'd find different things that are appropriate for regular vs. honors students.
Things to watch out for: None that I can see from just looking through the activities superficially. This book is fabulous.
* Graphic Algebra: Explorations with a Graphing Calculator from Key Curriculum Press is a nice workbook with a lot of nice word problems. I think the contexts are relatively realistic (although they're not always flashy), and they scaffold it well to build up to various types of graphs and functions -- quadratic, rational, exponential functions. Besides building a solid understanding of graphs, equations, and tables, the focus of this workbook is to allow kids to navigate their graphing calculators with ease, so they've also provided ready-to-xerox handouts that work specifically on those tech skills, asking kids to analyze the function (Trace and Zoom, that kind of thing) from a graphical perspective.
What I liked about it: If you work with your kids (maybe 9th-grade level, since there is some function notation in there) sequentially through all of the problems, I feel that it would be an excellent preparation for the more complex analysis that they would have to handle in high school. It provides a good amount of depth for the topics it does cover, and the word problems provide a smooth transition into/motivation for graphical analysis. You can also adopt it for use with higher-level kids, but in the interest of teaching time you probably would have to condense the explorations for those older kids...
Things to watch out for: There is almost too much scaffolding, down to setting up tables for the kids. If I were to use this book (which I totally would do), I'd keep the word problems and take out most of the excessive scaffolding, so that kids are left with some struggling room. The questions themselves are good. If you're already pretty familiar with the applications of these standard function types, some of the word problems are not going to be new to you. (But, it's definitely a super nice tool set for less experienced algebra teachers!! And, for me it still provided a couple of new ideas for new contexts that utilize the same-old functions.)
* Real-Life Math Problem Solving by Mark Illingworth is a workbook that is truly story-based. It's designed for younger children (maybe 6th-grade? ...Also applicable to 7th-graders as intro to various algebraic methods...), and I think it could be excellent for what it is. The stories are definitely charming (if a bit "young", some of them) -- they make no claims to be super realistic, but they're half children's stories and half word problems -- and for me, that's totally part of their charm. :) They remind me of those cute Alexandria Jones stories, whose context is as important as the actual math for keeping kids' interest.
What I liked about it: The really nice thing about these story problems is that they make no mention of a strategy to use. The kids can use whatever strategy it is that they wish/need to use, in order to solve the problem. --It also means that the kids are absolutely forced to read through the entire problem in order to figure out what's being asked, which is great practice for higher-level problem-solving. (Believe me; I tried skimming through the problems, because I myself have a terribly short attention span. Skimming doesn't work. They're not formatted like normal word problems where all of the info can be extracted at a single glance.) I also liked the author's suggestion of letting the kids keep a problem-solving "portfolio" of these problems and to work on them consistently over time, maybe once every couple of weeks.
Things to watch out for: Some of the stories are a little confusing at parts in the way that they are phrased -- especially because they give you quite a bit of not straight-forward information (which is a good thing). The ideas are usually great, moderately complicated, and pretty fun, but I think they need to be edited a little bit in order for your kids to totally get what info's being given. If you use these, definitely do the problem beforehand and check the solution in the back, because what you think the problem is saying isn't necessarily what is meant by the author.
* Spatial Visualization by AIMS Education Foundation (which I used extensively last year with my 9th-graders) is an awesome activity book for 3-D visualization. You can use it with physical manipulatives or virtual manipulatives a la this applet.
What I liked about it: Super awesome intro to 3-d unit; kids really "get" after this that surfaces usually have opposing surfaces (which I think is extended in higher-level math to show that the net surface area vector of any closed 3-D figure is zero), and what volume/surface area mean. Plus, they really love the activities!
Things to watch out for: At least in the version of the book that our school has, there are noticeable errors with the provided answer key for surface area and volume. Need to do the problems yourself to have a proper answer key. Also, since they give you a bunch of different problems for every visualization skill, you should be sure to pick-and-choose problems as to scaffold/make the content accessible while keeping students feel challenged.
* Modeling Motion: High School CBR Math Activities has some lovely hands-on activities that seem pretty cool, if you've got some motion sensors sitting around at your school.
What I liked about it: There are various activities that seem very do-able inside the classroom. You don't need much else than the motion sensors and some easy-to-get supplies. I've used CBR once in grad school (to try and create motion that mimics the given graph); it was pretty cool and generated good discussions.
Things to watch out for: I don't have enough experience with CBRs to really judge whether the instructions are sufficiently detailed. And I'm pretty sure my current school doesn't have CBR's. :(
Stay tuned. I'm going to keep looking around... Maybe at math videos next time!
Nice collection! It's interesting how this list reflects on the publishing industy's flight away from supplementals like these. Why, (wheeze, insert dentures) back in the old days, publishers like Dale Seymour had hundreds of titles in print! And now, they mostly focus on the comprehensive texts. Makes it harder to build what works for you out of the stuff on your shelves.
ReplyDeleteI think these little booklets are a more natural idea. It's much easier for me to imagine an author (or a few authors) having developed expertise with one particular topic and publishing something about it, than it is for me to imagine the same people publishing a huge collection of consistently interesting/effective teaching material.
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