Visual Patterns, Estimation 180, 3 Acts, Desmos, Which on Doesn’t Belong, Open Middle, Would You Rather, etc etc. I could create a list of awesome sights that provide a wealth of activities and tasks that promote learning for all students, but that isn’t even true. Don’t get me wrong, these are incredible resources- and while they can be stand alone I am beginning to wonder if they implemented in the best way possible.
I am not saying I have all the answers or even know how to use this great online bank of resources to its fullest potential, but I do know that they provide great ways to create your lessons into something real and meaningful to all students.
One site I use heavily when I am teaching 8th grade algebra is Visual Patterns. I like going from a visual representation, to a table, equation and graph (although there are many times I don’t go as in depth). From a teaching standpoint, is there a a difference in these two visual patterns?
Most of you will say no, and the task of drawing the next figure or five would seem fairly easy to most students. While the rate of change would seem obvious to many of us, it isn’t always so apparent to students, especially those with disabilities. While the physicality of drawing the next figures may appear to make this concrete, for many students that is abstract. I prefer the first example because I can bring out my Legos and allow students to construct the pattern (and I prefer the Legos because they will stick together- blocks tend to fall down a lot “accidentally”). Providing that opportunity is important, having resources available and accessible for any student who needs it. Will all students need it? No, but we need to get into a habit of having the resources available before a student asks for it or we realize we need it to help a student understand the concept.
When you use this is just as important. While these can stand alone and fill gray space in your class period, I think they should be purposefully implemented. Students will gain more from these activities if they are working on equations, graphs, etc in the daily lesson than if this is done before a probability experiment (I know, that’s a far stretch but I have seen things randomly thrown into a class or lesson because it catches the teacher’s eye). Instead of assigning 20 linear equation problems as homework, would creating 5 visual patterns and their solutions be as effective? Which assignment would create the best understanding? Those questions are also student dependent, but I feel that the creation of VP problems by students far outweigh a general procedure assignment. Don’t get me wrong, purposeful practice is needed for mathematics, I don’t think that we need to assign as many problems for it as traditionally thought. The format should also be changed, Dan Meyer had a good read on his blog here.
Speaking of Dan, his bubble wrap is another good example of how we should provide opportunities for students in great math tasks. I agree with Andrew Stadel that bubble wrap should be accessible to students for this task, and I have even modified the lesson in my classroom to not show a time for Dan popping the first sheet and allowing students to generate their own time. While this changes Dan’s final times, it also allows students the opportunity to justify their answers with mathematical thinking. It also provides an extra “bonus feature” of analyzing times for each student and considering the variability.
Every year in the classroom shows me how our current system is failing a large portion of our students. The gaps in knowledge are becoming larger- and is a who’s who of Nix the Tricks. Students have fewer and fewer experiences in mathematics, mathematical thinking and problem solving. They have become more adept in hiding these deficiencies, those that aren’t are those students that are making your hair gray. We can’t blame the students, this is a result of many factors.
We can’t hate the players, we need to hate the game that mathematical education has become. We need to change that game, provide students with opportunities they need to be successful. Design your lessons for your struggling learners, have resources out and ready before you even begin. All of your students won’t need them, but you may be surprised at how many will use them.