Have you ever had one of those moments when you’ve just savored the simplicity of what was going on around you? I had one of those moments just the other day…
I have lived on this Island my whole life and my mother has lived on the same lot of land her whole life, which is where I grew up. My husband, the boys and I popped in to visit my mom and dad just the other day and they told us that we had to come down to the shore to see something. Mother Nature had quite a little surprise – something none of us had ever seen before. There were thousands and thousands – maybe even millions of silver-sides which are little fish – like minnows. It was almost biblical, if that makes sense! What was cooler though, were the thousands of mackerel fish who were following and feeding on the silver-sides. These fish were schooled in the water where I grew up swimming and still do swim sometimes. The water was absolutely black with them – it was amazing! And you know the saying, “When life gives you mackerel, get the fishing pole!” Well, at least I think that’s the saying Regardless, we grabbed the fishing poles and my boys (Hubby most of all, I think) had a fantastic time reeling those fish in one after another, releasing and catching again within seconds.
Now my brother and I, we like a challenge. He had already caught quite a few mackerel with the pole, and so we decided that there were so many fish we could catch them bare handed. Now, I’ll spare you from the long and drawn out hour that followed, in which many different strategies were tried, re-vamped and tried again. The story ends, though, with each of us catching two mackerel – without using a fishing pole. I could totally survive in the wild…ya probably not. Nowhere to plug in my hair straightener! But it sure was fun. The reason I’m sharing this, is because at one point I just looked around and observed the fun that my family was having. It was a perfect Island evening; a small, yet memorable moment. If we had decided it wasn’t worth the effort to head down to the shore when my parents suggested, none of it would have happened. It would have been a completely missed opportunity. Fish, literally jumping out of the water and no one there to catch them. Make sure to grab some of those moments for yourself this summer (and of course in the classroom next fall)!
So, while we’re on the topic of seizing opportunities, it’s crucial to grab those teachable moments in the classroom, as well. In Accessible Mathematics: Ten Instructional Shifts That Raise Student Achievement, Shift #6 is to build from graphs, charts and tables. It may seem like a small thing, a simple thing. I know it does to me. However, I also know that I’ve missed tons of “moments” by not really delving into all of the data in a table, only using the information that was most pertinent to the problem and essentially ignoring the rest. I’m embarrassed to even type that, but in a 38 minute block there isn’t always time to answer questions that haven’t even been asked.
Leinwand’s suggestion for building from given data, is to ask the question, “So?” and see what happens. Rather than just answering one or two straightforward questions, ask your students “So?” Of course it depends on your data, but the example that is given has to do with ticket sales for a concert. A typical question in a text book could be, “Which musician sold the most tickets?” At this point, I would let my students independently answer this simple question and they’d move on to the next problem. Well, now I’m beginning to see that would be like looking at all of those mackerel swimming around and saying, “Cool!” without actually trying to catch one – missed opportunity! A simpler experience, for sure, and MUCH less satisfying.
In this author’s opinion, when teachers begin to ask, “So?” and their students get used to that questioning, crazy things happen! Crazy-good things. Thinking, questioning, and deeper understanding and appreciation of mathematics. So, with a problem about ticket sales, questions that they could come up with could be:
-How many tickets were sold altogether?
-Why is So-and-So the most popular?
-Which concert would be the least popular?
-How many more tickets did Concert 3 sell than Concert 6?
-Which concert sold the closest to 300 000 tickets?
-What percent more tickets did the most popular concert sell, than the least?
I could go on. The point is, if you’re going to require students to refer to a table, chart or graph for answers, that should be only the beginning of a line of questions (that should come from them, ultimately) about the data so that they care more, engage more and so that you can build in every opportunity to extend number sense (which is Shift #5).
I teach grade 7 and there’s always at least one student who wants to know why they should care about what we’re doing. Why does is matter? So what? These students will be the strongest, I believe, in answering the, “So?” question. I know that I’ve often chosen to have students answer more problems rather than really extend a problem in the way Leinwand suggests. I have my reasons and I don’t think that it’s a bad thing at all. What I can clearly see now, though, is missed opportunities. I have been guilty of getting wrapped up in the three IEPs, two behavior issues and other multiple needs within my typical classroom, trying to meet a vast range of needs, at both ends of the spectrum. Honestly, extending data rich problems has not been at the top of my priority list for teaching math. That’s exactly why I read professionally in the summer. I don’t have students in front of me. It’s NOT overwhelming to think about, “How could I do this?” At the moment, I can think clearly and objectively and see the value in what Leinwand is arguing.
This shift (and a few others, actually) have catapulted me into deciding to make a much more significant change in my math classroom for next year. I have started reading Minds on Mathematics: Using Math Workshop to Develop Deep Understanding in Grades 4-8 and the content supports the shifts in Leinwand’s book, but it actually offers a workshop format for teaching math. I’m loving what I’m reading so far and I know what better problem solvers my students will become if I can make this shift. Anyway, I don’t want to put the fish before the pole…so more to come on this later…
Are there any teachers out there who routinely ask their students, “So?” Please let us know how that works and what it looks like?
I had mentioned this book Accessible Mathematics: Ten Instructional Shifts That Raise Student Achievement
in a previous post and I had also mentioned that I would be following up with my insights as I read the book, throughout the summer. (Thanks for the inspiration Andrea @ For The Love of Teaching Math.)
I just read the introduction, which was quickly curtailed with, “Mommy…Mommy…Mommy…you play Legos with me?” How can I say, “No” to that?
So, I’m only three pages in, but I’m loving the common sense feel so far. This is what I have surmised. It really is the instruction of each teacher in the classroom, that will determine much of the success of the students in the room. If we engage them, or bore them; teach at them or to them; consider their learning needs and our delivery of the material. It’s our job and it truly is all up to us! No pressure…
When you stop and think about it, a teacher really could mess up a class of students, without too much trouble! I know, it’s a scary thought – but stay with me. Just imagine for a moment, that you are not the forward-thinking, best practice seeking professional that you are. What if you made your class copy out each problem, word for word, from the book before answering it? Think about all of the time wasted with this “instructional choice”. How much more success would your students potentially have if more time was spent on instruction, rather than copying? It’s a simple example, but I think that you catch my drift! So, I’ve come up with an “instructional mantra” if you will, to remind teachers of their part in determining the success of their students, “I Got The Power!”
Okay, I can’t just drop a line like that without a musical interlude – so here you go… Let’s meet back here in 5!
Seriously though, we do have the power! I know, that so much of our students’ success lies with them – their efforts, their attitudes and their aptitudes. However, you can’t downplay, the fact that we set the stage for learning and it is up to us how each and every minute in our classrooms is spent. Personally, I do think that I make the most of my instructional time – to the best of my ability. I am human, of course, but I always try my best. That being said, I also know what I need to work on. I need to focus more on problem solving strategies and giving time for students to actually struggle through problems. I find it frustrating, because they get frustrated so easily and shut down at the drop of a hat. I need to figure out a way to instill some perseverance in to the youth of today! I also know, that I need more time built in to my lessons for review.
So, what do you think?
Are you using the most of your time, each and every day, to the best of your ability? Do you feel as though you are using adequate time for instruction? How much weight do you believe should be put on to teachers’ instruction, in determining the success of their students? I’d love to hear your thoughts!
I was pleasantly surprised just the other day when I went to collect my mail at the post office, and found that my prize from a blog contest that I entered had arrived! You know that I love PD and professional books. Well, I won a book called Accessible Mathematics: Ten Instructional Shifts That Raise Student Achievement, from Andrea, over at For The Love of Teaching Math. (Thanks again, Andrea.) I haven’t even gotten to sit down and have a really good look yet, but I’m dying to find some time to delve in. The ideas in this book are not about completely revamping your program, but making small shifts in what you already do. Some phrases that jumped out to me in reading the book’s description: “practical” “common-sense ideas” and “streamline your teaching”. Yes, please! I’ll take one of each!
I always read at least one or two professional books over the summer – and it looks like this is going to be one of them! I know, I know. Summer time is a time of rest and relaxation, but for me a big part of the summer is also working on improving my craft and finding at least a few new ideas that I may incorporate into the next school year. (I think it’s because I still feel so lucky to have a job, with the current state of education in my area, even though I’m almost seven years in.)
Anyhow, I’m not going to commit to a “book study” on the book. I’d love to, but I think that it’s just more than I’d like to sign up for – I’m running low on energy! I know that many of you may be in the same boat. However, this is a slim, little read at under 90 pages (there are multiple Appendices in addition to that, though). Very do-able if you are looking for a professional math read this summer. It also has examples from across the grade levels, so if you teach math – you’ll find something useful to take away, I’m sure!
I’m excited to start reading and seeing what common-sense ideas it has to offer me! I’ll be sure to share my main takeaways from the book in future blog posts this summer. If you have read the book, or would like to – please be sure to comment from time to time to tell me your thoughts. A conversation about these 10 shifts would be great.
Thanks again, Andrea. You’ve made choosing a summer reading focus pretty simple this year! I hope that all is well in your state of Oklahoma.
Do you read professional resources in the summer? Do you have a book that you could recommend? Please leave a comment with the title and I’ll add the links to the bottom of this post as they come in!
Some of your favorite professional reads: