Book Review: Accessible Mathematics - 10 Instructional Shifts That Raise Student Achievement by Steven Leinwand

Things I like: I read this book quite quickly. It took about a week with reading only 20 minutes a day. In addition to being short, it has some fantastic ideas that are backed up by oodles of research. All of the "shifts" he writes about are things that a good math teacher should do:
1. Incorporate cumulative review each day.
2. Learn from reading programs: ask questions about inference, focus on process rather than the answer, etc.
3. Use multiple representations
4. Have language rich classrooms
5. Take all opportunities to develop number sense.
6. Build from charts, graphs, and tables
7. Increase the natural use of measurement throughout the curriculum
8. Minimize what is no longer important
9. Embed mathematics in realistic problems and real-world contexts
10. Make "Why?" "How do you know?" "Can you explain?" classroom mantras.

All fantastic things. If all math teachers did these things, I probably wouldn't have created this blog and there probably wouldn't be this huge education reform (with regards to math at least).

The book also has some neat articles in the appendix. The one on what we can learn from Singapore Math was quite interesting.

Dislikes: Not much really, mostly a perspective thing. This is not really a "Break Tradition" book. I got the feeling that it would take a traditional teacher, and turn him/her into a traditional teacher that uses research based methods. Good, but not my cup of tea - it's peach (yum!)

I recommend this book to all traditional math teachers or teachers that are unfamiliar with the research regarding these ideas. Good ideas to keep in mind as I break tradition.

Anyone else read this? Your thoughts about it? What other "shifts" would you recommend Math teachers do?

Stuff I'll Be Posting On This Blog

Now that I've put oodles of things on this blog, I feel like I can actually post stuff I've wanted to get going. With the base laid out, I can put down posts that will relate to my mission: to overcome the traditional math teacher. Some categories that will show up are as follows:

Book/Article/Literature/Blog/Media Review - Whenever I read/hear/watch something that has effected my teaching, I'll post it and share my experience. I'd love to hear from others on their thoughts.

Break Tradition Idea - As gems come along, I'll post them. The education world is soooooooooo incredibly full of ideas, I'll probably only post stuff that seems good to me.

Classroom Experience - Ideas are great, but if nothing is tried out in the classroom then they essentially fell on deaf ears. I'll try things out and share how it went. You should share your experiences too!

Resource - If I find something I think is awesome, I'll post a link to it. These will be similar to the Review category, except they will have resources for teachers.

Game - As I find games to try out in the classroom, they'll go up!

Other - For other stuff duh! (Most likely comics and memes).

Is there anything else you'd like to see me post and write about?

Teaching Philosophy: Status as of June 26, 2013

If there is only one thing I've noticed with writing out my story, it is that my teaching philosophy is very wishy-washy. The whole traditionalist to purist to applicator happened in just 4 years. All sorts of things are probably going to change. I probably won't change that I like to teach applied mathematics. I like it too much. It's like getting a taste of peach rings each time I see students using math to analyze something and come up with a conclusion they can justify. I'll put down a few statements I currently believe to help keep track of where I am and where I've gone. I want your thoughts on any of them. I welcome multiple opinions.

1. Students learn math best when it is "real". I put real in quotations for a reason. I've found that it doesn't matter how realistic the situation is that you've presented. You could be designing an actual school or determining the cost of an actual mortgage payment. If the students don't see the task as real to them, then they will not be engaged and want to learn about it. That being said, the task doesn't have to be real-world at all. Finding out how long it will take to mine down to bedrock in minecraft is far more engaging than finding out how long it took to mine the London tunnel. Don't worry if your task does involve something real but doesn't relate to students. You can get over that hurdle by getting the students invested in the task like Dan Meyer does in his 3-Act Math. (Genius work on getting students interested in real world situations btw.)

2. Students need to use knowledge in order for it to stay in their wee little heads. Even when you're using real tasks all the time, if students haven't used the Pythagorean theorem in three months, chances are only one student will think to use it in situations where we'd obviously use it. The problem with math education is that there are hundreds of little tools (tricks) we can use, students often don't remember them all or try to use them when they shouldn't. I agree with Steven Leinwand in his Accessible Mathematics when he wrote that we need to incorporate cumulative review into every lesson. I'm going to try doing it for the start-up activity this next year unless a better idea comes up. Students also need practice, but not 20 "problems" for homework every day. I like using less "problems" that require deep thought on part of the students.

3. Students acquire a deep understanding of math by analyzing situations, coming up with conclusions, and debating those conclusions with others. There is something magical about when students argue mathematics with one another. Maybe I'm just a sick, demented man, but I love those arguments. It shows that students are thinking critically. It shows that students are thinking about the mathematics. It shows that sometimes (most of the time) in life, there isn't a clear cut best answer. Students should be doing this often. They need to analyze, come up with conclusions, and defend their conclusions. It brings up so many misconceptions that get corrected. 

4. Students learn math best when they use multiple representations. I know there is a butt-load (that's a real measurement) of research on this. I agree with it. Students should be using graphs, algebra, tables, words, etc. to come up with their conclusions. It allows students to become fluent in many ways of communicating.

5. Teachers need to connect with students. I like smiling, getting students to laugh, and being their friend too much for this to not be a part of my philosophy. If students like the teacher, they are willing to work at things they normally wouldn't. It is a lifesaver in the classroom when you have a less than exciting lesson planed, but you need the students just to do what they're told. You can fall back on your report with the students and get to the work. I realize that every teacher is different and some personalities don't jive, but teachers need to connect with at least some of their students.

Please, share your thoughts. What would you add? What would you take away? What do you think should change?

Story Time: From Purist To Applicator

[...Continued from previous post - I figure I should break it up into chapters for reading convenience]

As I was finishing up my student teaching I got the opportunity to go to a Teacher Fair to try and get hired. I stopped by all the school district tables that interested me. I did like 3 different screening interviews there. I had a break while the fair was winding down and so I meandered to see tables. I came across one that had a guy talking about using a dart gun and Rube Gholburg projects in his math classes. I got instantly interested. We started talking, and it turned into a really good conversation about how math should be taught: with hands-on, real-world tasks. We clicked and the interview went smoothly. I was hired on for the next year within a couple weeks. The man turned out to be Noah Williams. He is a truly brilliant man. I honestly think he will be a man to look out for in the future. He became my coach as to what to use to teach math in the middle school. I was converted to an applicator of math. Everything we do in math has purpose in the "real" world. Math is the Master Tool that we can use in any discipline to analyze and make decisions.

I started the school year with almost no resources. There were some books, but they were typical math textbooks and had almost no application to the stuff they taught. So I had to come up with my own activities and documents for what turned out to be 4 different grades of students: 6th, 7th, 8th, and 9th graders. It was perhaps the most difficult thing I could have possibly done for my first year of teaching, but I wanted to start fresh with nobody telling me what to do to teach except the Common Core State Standards. I used them as a guideline for what to teach and I gathered ideas wherever I could find them.

I searched and searched and searched for hands-on activities to teach students math. I bought over $100 worth of books that claimed to have projects and hands-on activities. Some did and some didn't. It was a gamble really. I wouldn't say any one of them was particularly bad, they just weren't what I was looking for. I'll do a quick review of the ones I liked in another post. (This one is dedicated to story time:))

I spent time searching the internet for resources. Holy freaking cow! There are soooooooooooooooooo many websites, and soooooooo (notice the fewer o's) many of them are complete piles of ****. (I guess that statement depends on what you're looking for. If you're looking for non-traditional material, then it is). Truth is, I wasn't looking in the right places. I didn't know what to look for. I wasn't part of online communities. And honestly, there aren't that many AMAZING sites out there that appeal to me. I feel like everyone has their own ideology on what makes a kick-butt curriculum or lesson, and none of them match up to what I think is awesome. It's because I get bored with things that are "Mathy" like graphs and numbers. Other people think those are interesting and that is cool. We're different people. I haven't been really connected to others with twitter and blogs, but I'm working on getting out there. I'm hoping to find more people like me.

Anyways, I'll post favorites and my thoughts.

Have you struggled finding resources that fit what you want? How do you find them?

Story Time: From Traditionalist to Purist

Now that I've said my peace about traditional math classes, I'll continue my story.

[BTW: When a blog post has "Story Time" in the title, you are safe to assume that it include some narrative about my life as a Math teacher. If you're looking for just resources that I'll be posting, just look for "Resource" in the title.]

With my first 2 1/2 years of college I thought I'd be the most ballin' Math teacher. I was going to explain things so well students couldn't possibly misunderstand. I was going to make my grading system so easy that students couldn't possibly fail and everyone can get an A. Homework would be short and to the point. Class time would be perfectly structured so students could have some free time to talk.

 I even had an epiphany one night that school could be restructured so students wouldn't have semester/year long courses, but would go to one or two week long courses that taught a little bit of information. Students would attend what they needed to and get checked off by the teacher of the course. Kind of similar to how Boy Scout merit badges work. Students would pass of their full classes (i.e. Algebra 1, English 9) after they had been checked off the list of required mini courses. Then students can go at their own pace and finish as early as they wanted. Brilliant!

As you can see, I was already had anti-tradition thoughts, but I was deeply entrenched in the tradition. I just wanted to change a few things. I wanted students to just do their algorithmic skills just long enough to beat an evaluation and then they could promptly forget about it. No critical thinking or problem solving involved.

I didn't realize how engulfed I was in tradition until I started taking actual Math Education courses and Math courses that required proofs and analytic skills. This was a huge mind opener: Math isn't just computing stuff!?! I don't have to do things a certain way? There is actual logic involved? (These classes helped me find my love for logic and logic puzzles. Man, logic puzzles are as delicious as beacon wrapped sausage!) I learned what Pure Mathematics was.

Then I had a professor, Jim Cangelosi, who was hilarious and ragged on traditional math classes all the time. He had his own method of seeing Math education and how to go about it. Jim gave us tasks to do that required us to develop our own knowledge, to talk with others, and discuss math. This was my first introduction to something that was non-traditional... and it BLEW MY FREAKIN' MIND! I was like: Whoa! and then: Whoa!, and lastly: Whoa! Like the turtle from Finding Nemo.

After a few days of those lessons, I realized that my whole life was a lie... I started questioning whether my parents were really my parents. I wondered if life was really a dream in some Fish's mind on a far away island and Link might wake him at any time now. I started thinking that if I were to wake up, then my children would come back to life.

J/K. I know my parents are really mine.

Anyways, it was from those classes that I realized that my entire math education was a complete joke. Schools don't teach real mathematics. They teach a strange demented form of math where logic and reasoning aren't needed, let alone wanted. I decided that in my classroom we'd be learning math the way it should be: logically with axioms, undefined terms, and proofs. It was going to be awesome. Students would have such an understanding of Mathematics in its purest form as to surpass all previous generations!

[To Be Continued...]

How about you? When did you change from being a traditionalist to anything else? Were you never a traditionalist? Did you have that "Holy Cow, I've been messed up my whole life!" moment?

What's Good About Traditional Math Classes?

Okay, I'll admit that the traditional math class isn't 100% messed up. It is more like 99% or 98%. It has some things going good for it:
1. Students should practice the algorithmic skills involved with Math.
2. Um... order is important I guess.

I wrote #2 because I felt bad that I could only come up with one thing. Since I could only come up with one real thing that traditional math classes have going for them, let's say that they are 99% messed up. Honestly, I'm having a hard time coming up with more things I like about traditional math classes. Maybe it is because I am so blindly intent about not doing what they do. It isn't that everything they do is BAD per se, but that there are so many BETTER things that teachers can do.

What do you think? If you were revamping a math class, what would you keep from tradition?

Now, the enemy: "Traditional Math Class"

The whole idea of this blog is to take a journey through breaking the traditions of math education. I should lay down what a traditional math class looks like. Then we can know what the enemy is. Once the enemy is known it can be attacked.

The Enemy: Traditional Math Class

Summary: Traditional Math Classes have been running rampant for more than a century. They have destroyed children's hopes and dreams to do anything that requires mathematical thought by presenting math as a series of tedious algorithmic skills and deprives it of all meaning. Despite their devastating effects, they are present in almost every school. Due to the "tradition", most new math teachers start one right away and follow in the footsteps of their predecessors. Little can be done to stop them other than to phase them out slowly by converting those who are willing to change and teaching prospective teachers a better way.

Attributes: Traditional Math Classes are teacher centered. All desks face the board. The teacher lectures, expecting students to shut up and listen, and the students take "notes" (typically of the form of just writing down whatever the heck the teacher writes down.) The teacher explains a concept void of any meaning, does some practice "problems," and then the students do some practice "problems." The students have homework doing more "problems." During the next class session, students correct their homework and turn it in. Only the final answer matters. The process does not unless the students are in elementary or getting help from the teacher. If that is the case, they better do it the same way as the teacher. The cycle continues every day. Teacher lectures, students take notes and do the "problems." The answer to the question "when will we ever use this?" falls typically into the categories A) Because you'll be tested on it B) So you can learn more math (like calculus) or C) Because I said so.

Reason for Termination: Students avoid math like the plague. They shy away from anything that might require advanced thought because it is too much like math. Students fail to enter into STEM fields of study. Students avoid problem solving.

Defenses: Tradition. Perhaps the most sturdy of fortresses, the only way to destroy it is to run. Run as far away as you can. If you forget a tradition, it will die. Unfortunately, too many people know of the Traditional Math Class. Each prospective teacher has had some 16+ years of experience with it, and think that it is the only way to teach students Math. We must persevere in convincing teachers to teach Math a different way. If we can get teachers to forget the tradition, we may survive its relentless assault.


Really, this isn't everything, but I wanted to get a picture up of the enemy. Further details will be added in other posts.

Story Time: A Bit (lot) Of Background

(I don't know why, but I feel the need to give background to let people know where I'm coming from. No one is going to read my background. Why should they care? Well, I wrote it anyways!)

Our experiences make us who we are. Mine made me into a math teacher. No, I didn't have an inspiring teacher that made me want to be a teacher. Even though I had some good teachers, none of them left any desire to teach. In all honesty, my Math teachers were rather horrible at inspiring me to do anything with math. Thank goodness math was a cool thing in my family. The particular inspiration to become a teacher came when I realized I never wanted to grow up.

I decided that I wanted to become a teacher the summer before I started college at Utah State University. I got to thinking a bit (which teenage boys do seldom, but I was having a lucky day). I had always entertained the idea of being a teacher, and during that summer I realized it has exactly what I want:

1. I don't have to work in foods or customer support (often). I worked fast food and ride operator at a local amusement park. This taught me a wonderful lesson: people suck way bad. Particularly adults. I don't know what happens between teenage years and adulthood, but people become real dicks. 

"WHAT!?! You put in a complaint that I didn't GENTLY put your bag of food on the counter!?! It's freaking Arby's! I was running around like crazy getting everyone else's food together!" "You can't ride the swings without close-toed shoes. I don't care that you waited in the line for 20 minutes. It's not my fault you didn't read that gargantuan sign at the entrance to the ride. Stop shouting sir, it won't change anything... FINE! I'll call my supervisor so HE can tell you the exact same thing."

Yeah, adults suck. Teachers get to spend almost all of their time with adolescents? Sweet! If they give me a ridiculous time I can at least get a counselor to do something about it.

2. I don't have to work outside. Man, this one summer I worked for a general contractor doing random jobs. These included the following:

Docking and shooting up some 50 50 lbs pigs with drugs. After injecting them, I had to carry them around the corner an place them over a 4 foot high fence. Ever picked up a 50 lbs bag of salt? Now imagine it doesn't want to be lifted and starts throwing its weight around. Stupid pigs. They don't know what's good for them. (Actually running away would be good for them. My boss already had all the meat from those pigs sold before they reached full size.)

Picking up every single rock in an acre plot of land.

Moving rocks from one location to another.

Drive re-bar into concrete.

Destroy fences while being careful the cows don't eat the old barbwire (why cows eat barbwire is beyond me).

All of these were outside in the summer in the sun that burned my bald head (yes, even at 19 I was quite bald.) I decided that I better get an education to avoid skin cancer of the head.

3. I don't have to change my schedule. I love having my summers to do what I please. Perhaps the most important part about having a school schedule is that I will be out of school when my future kids will. I want to be there with them playing in mud, going to the park, eating snow cones, and terrorizing Mom. (I can't wait for when my wife gets annoyed yells at me to go play outside. :)) Honestly, this is perhaps the most important cool thing about being a teacher.

4. I get to teach. I absolutely helping other people understand stuff. Maybe it is because I like being smarter than everyone else. Maybe it is because I like seeing the light bulb come on. Maybe it is because I like hearing the sound of my own voice, but whatever the reason I like teaching.

Teaching looked like the best possible thing I could do with my life and so I chose it and went to school for that.

I Guess I've Got To Start Somewhere

Sup Y'alls. This is Matt Jones, but the name you call me isn't that important. My students call me Matt, Mr. Matt, Mr. Math Teacher, Hey you!, etc. You can call me Dufus if you really want, but I don't recommend anything that would greatly offend others. They might grab their pitchforks, torches, and come kick your digital butt. Minor offenses are okay though.

Anyways... I'm starting this blog to share my experiences with readers about breaking traditions that teachers have had for many years now - specifically Math teachers. I also want to share resources and ideas I've collected to kick traditional math classes in the face with metal spiked cleats. Many of these resources and ideas won't be my own, but I'll try to give credit where it's due.

All great journeys have to have a beginning. I'll post that next.