I have decided to make this my last post on Accessible Mathematics: Ten Instructional Shifts That Raise Student Achievement. I have 2 other math books that I am reading (What’s Your Math Problem? Getting to the Heart of Teaching Problem Solving and Minds on Mathematics: Using Math Workshop to Develop Deep Understanding in Grades 4-8) and would like to make some comments on those as well! SO much to say – so little time! Anyhow, I am going to chat for just a bit on shift #9, which is one that is important to me, but that I struggle with at times:
It is extremely important to me to try my best to find connections to the real world and have answers ready when students ask the question, “Why do we have to know this?” And teaching grade seven, there is no shortage of students asking this question. It’s a good question, though and it’s my job to have an answer ready which is more than just, “Because you’ll need to know it for grade 8.”
Some concepts are much easier for me to find realistic connections to than others. I struggle with the first unit that we do, which is coordinate geometry. I know that reading a map (longitude and latitude) is an obvious example, but what about GPS? Realistically, can’t many people use the GPS in their vehicle or on their iPhones to get where they want to go? How many people on a daily basis need to use longitude and latitude? A yearly basis? I know that certain professions do for sure, but is it something that people outside of those professions NEED to know? I’m talking about the average person. I’m not saying for a moment that map skills like understanding longitude and latitude are unimportant. However, I personally have never needed that skill in my own life. Ever. (Outside of my profession, of course). I did find a video of an archaeological dig (it’s a little pixelated though) which somewhat shows people using coordinate geometry in a different sense – but what if you’re not in one of those jobs either? Hmmm…
Switching gears, what about teaching students the formula for area of a circle – when will they USE that formula in real life? Of course, if they’re making a table-cloth and need to know how much material to buy…but wait a second…how many people are at home making their own table cloths? And in real life, if we need to know something, like a formula, what do we do? Google it, of course. Within seconds we’d have that formula at our fingertips. So again, when was the last time you used the formula for area of a circle? I’d honest to goodness LOVE to know, because again – I personally never have (and am searching for more real life examples).
Probability? You bet!
These are things that I can easily relate to with examples from my own life. For instance, I brought in my bills one year when we were doing integers and my students weren’t grasping addition and subtraction. When I showed then my debt and then my payments – it started to make a bit more sense. Real life! I just wish that every unit was as easy to find examples for as integers!
I guess what I’m saying is that this shift has made me reconsider something that I’ve thought of often: How can I make math more “real-life” for kids? You may say it doesn’t matter – solving problems is solving problems. Who cares what the actual problem is about? Well, they do, actually. Our students. They want to solve problems that may actually exist for them some day. Think about it. How much time would you care to devote to solving a problem of any sort if it had no context, or importance to you? I’m guessing not much. Why? Because it doesn’t matter, so why would we care?
Coming up with “real-world” examples and problems for my students is something that I’m working on and will continue to work on, as I know it’s at the heart of student engagement and understanding of math.
How do you try to bring the “real world” into your math classes? I’d love to hear what you have to say!
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 hope that my Canadian friends had a lovely Canada Day and I hope that my American friends have some fun plans for their upcoming holiday as well.
Friday was my last day at school and I’ve never left my room so tidy and organized! I guess that’s what comes with more teaching years under my belt! I will have only 18 students next year in my homeroom and the entire group coming in is just a lovely bunch of kids and so I feel completely at peace and ready to relax this summer.
I must say, I am making the most of my time off so far! Last weekend was busy. I went out for drinks and took in some live music with a few teacher friends. I love to just sit and chat! We had a family BBQ at my sister’s on Sunday. Hubby and I went on a “park hop” with the boys on the holiday Monday, driving around letting them play at different parks that we don’t usually get to. A picnic lunch, ice cream and fireworks in the evening made it “the best day ever” in the words of my five-year old. Who needs Disney World? Like I said, I really feel like I’m making the most of my time off so far.
Of course, part of my summer routine (as I’ve mentioned before) is to do some professional summer reading. Some day, I will begin working toward a Master’s in Education, but until then, I’ll further my own learning in this way. I’m just about finished of Accessible Mathematics: Ten Instructional Shifts That Raise Student Achievement and it really is a super little book, recommended by Andrea @ For The Love of Teaching Math. Last summer, I read and posted about a professional math resource as well, Guided Math: A Framework for Mathematics Instruction and I incorporated some of author Laney Sammon’s ideas into my classroom. I’m actually seeing ways to mesh some of what I did with her book last year, into what I hope to do in my room next year, which is awesome!
Now, I’m not going to give you a play by-play of every single chapter in Accessible Mathematics, but I will pass along some of my take home messages in my next few blog posts (original blog post here). Actually, I’m super excited because I have two more math resources on the way that were recommended by teacher friends (What’s Your Math Problem and Minds on Mathematics should be arriving in the next two weeks) and a few others on my wish list:
So, Accessible Mathematics is broken down into ten “instructional shifts”. The first shift is something that I do, but need to do more of and need to do more systematically. The first “instructional shift” is to build more review into every class. I do review, don’t get me wrong. However, I am guilty of moving on at times, rather than looking back as much as I should, simply because of the amount of material we have to cover. I’m sure that you know where I’m coming from.
The way that Leinwand suggests using review is quick, practical and something that I know I can do. I’m going to try beginning each class with a five problem review. I’ll have students use a half scribbler for these review problems and may collect them periodically. However, I hope to gather the information that I need by circulating around the room, the vast majority of the time. Five problems, five minutes – that’s my plan. If it takes a student five minutes to find their scribbler – they’ll have to catch the review the following day (although that STILL gives me information on their organization and perhaps even signifies an avoidance behavior).
I find that getting classes settled can waste a lot of teaching minutes, especially when I’m teaching in a room other than my own or have a chatty class. Beginning class this way should settle most students more quickly (in theory) and get us focused for the amazing lesson ahead (I’m sure that’s what they’ll be thinking).
As far as material, I’m thinking about using multiplication/division facts, fractions, integers – really hit home with the skills that I need my students to master before they leave my room, or that they were missing when they came in. I also want to make more of an effort to go back to concepts from previously taught chapters as much as possible to try to keep everything that we’re learning at the surface and let very little settle to the bottom of their easily preoccupied brains!
I have a few resources that I plan to use to address these review problems. I actually found a great (although old) resource when I was tidying up my room at the end of the year. It was a mental math resource from the board, from at least 8 or 9 years ago. Still good stuff, though. I also have a book called Seventh Grade Math Minutes that has some perfect material in it. I may also use the 6th grade version. And then, my actual math text does have some “Getting Started” problems that I could incorporate as well. That’s what love most about “Accessible Mathematics”. I am motivated to make some small shifts, and have been forced to do a mental inventory of my resources and how I may better use them. I don’t have to buy anything to make the shifts that I plan for September, I just need to use my time and resources in a way that (hopefully) will be even more effective!
Please add the titles of any other middle school math resources that you think my readers and I should look into. I’m hoping to be a part of a Math PLC (Professional Learning Community) in the next school year and so I’m collecting resources/titles. Also, please give me your best ideas/what you do to review in your classrooms. I’m open to ideas and methods that work, from you, the experts!
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: