Is The Common Core Just Misunderstood?

commoncorelogo-color2Please forgive me if you hate the words Common Core. I don’t try to go out of my way to write about something controversial, but I know the potential firestorm for this topic. My first question to all those that abhor the Common Core is:  Do you every wonder why the Common Core came to light? Although I have background knowledge, I quickly did an Internet search to see what explanations abounded. Terms popped up like, ‘college ready’, ‘consistent expectations for all regardless of zip code,’ ‘national standards,’ etc.

There are a lot of people, both in and out of the education field that hate that explanation, so it is not one that I will support in this entry. Preparing students for the real world, yes, obviously that is something that we focus on as much as possible, but what does that even mean? The meaning probably depends on whom you are speaking with. All I can offer is my interpretation. I want to prepare students to think critically and deeply about any problem, whether numbers are involved or not. My hope is that students analyze problems carefully and reflect seriously about all options before trying to attack any problems in the “real world.” I think the Common Core actually helps with that objective.

Please allow me to offer my classroom perspective. I have been teaching math to students for 15 years. 10 years was in an elementary setting, and the last 5 have been in the middle school.  Within that 15 year span, teaching philosophies (as well as several math programs) have come and gone. Throughout all of the math trials and tribulations, one consistency remained; students were not retaining the math. I know this is not just a phenomenon I have witnessed, because if it were, there would be no Common Core. The traditional way of teaching math would involve students learning an isolated concept. After learning it, students would study it for several weeks with lots of practice examples. The examples might be peppered with some derived textbook problems and culminate with a test. This is how I was taught and I know how many of you were taught as well.

Immediately after the test, many students would promptly forget about the past concept(s) and move on to another topic. Some of the details would re-emerge as necessary, but many students would notice that previously learned concepts drifted out of their minds after moving on to another topic. There was little transfer of knowledge from the temporary memory to long-term memory storage in the brain. Some students would retain rote procedures, and be promptly labeled as math people. Those who were unable to remember were labeled another way.

This was and continues to be a huge problem. Math concepts build on one another. They only have the opportunity to do so when students actively make connections from one concept to another in experiences where they witness the fluidity. For those who label The Common Core as fluff and not real math, please allow me to assure you that it was not designed to eliminate the algorithms. In everything I have studied, the algorithm (procedures we all learned growing up) is still the goal.  The difference between direct procedural teaching and problem based learning is that students receive the opportunity to investigate the why first.  The investigation allows students the chance to actively make mathematical connections with the ‘why’ to the procedure. Often, when students are given a problem, it creates the interest in the procedure that would never have been there if it were the only teaching point. What does this mean for our students? Instead of promptly forgetting procedural math, visual and problem based learning allows students to double down on their understanding and have the option to not only solve a specific problem in a unit, but provides students with tools to figure out how to solve all problems as efficiently as possible.

One of the largest obstacles of this philosophy is the incredible push back against it. This does not just come from parents, but also from fellow teachers. Change is hard, no doubt about it, but I have seen with my own eyes the difference between students memorizing a procedure versus deeply understanding why they are using it. The difference is stark. The reality is that the transition has not been easy and we all feel the growing pains together. But fear not…

I truly believe that I am a much better math teacher today than I was 5 years ago. I can imagine and hope I will be that much more effective in 5 years compared with the way I teach today. This means my students will be better prepared for that scary real world we love to discuss. I credit my continued improvement to the Common Core because of my virtual colleagues. Math superstars like Jo Boaler, Dan Meyer, Robert Kaplinsky, Fawn Nguyen, Yeap Ban Har, and Andrew Stadel were likely brought together by The Common Core initiative. Thanks to social media and passion, we now have resources that allow us to collectively and positively impact our students’ minds.

I accept that challenge. The question is…do all of you? If the answer is yes, please stop picking apart The Common Core or shuddering at the mere mention of the term as if it were ‘Voldemort’ from Harry Potter. The Common Core’s evolution came from student necessity. It is time that we work together to address the ongoing needs of our students, parent communities, and even the frustrations when we fall short. Two words should not undermine our purpose nor our passion that were actually developed to ignite them both.

It’s Summer Vacation and I Can’t Shut Off my Teacher Brain…

teaching and summer

This past year of teaching was revolutionary for me. After years of reading articles, books, and receiving tiny amounts of professional development that may or may not have made an impact on my brain, I evolved. No, seriously. I went from surviving the changes perpetually implemented by the powers that be to balancing those while making hundreds of my own. Granted some were successful and others, not so much…but I digress.

It seems that all of the pieces of advice that were dribbling into my brain finally congealed. Yes, I now have the big picture of what math instruction should look like, until additional research convinces me to change everything again.

I started this past year with one crazy goal. My goal was to make all of my lessons  fantastic experiences for both the students and myself. You know the ones I am talking about teachers. I am referring to class periods where you look around the room and every single student is engaged and no one looks bored. These kinds of lessons provide uninterrupted time frames where no one is staring at the clock; understanding is elevated, amazing questions and inquiry is running amok, and where students actually feel disappointment when the bell has rung. I wanted (ok, still do) every lesson to be like that.

After reading Mathematical Mindsets by Jo Boaler and taking two of her courses this summer, it fully hit me that an engaging lesson is the tip of the iceberg. I suppose I knew this already, but my understanding became deeper. Math instruction is not only about the individual lessons, just as math itself is not about the individual concepts. What my job is really about, is to help students to see math as a fluid subject. Students need to seek out patterns and find the connections so that one lesson (as engaging as it is) does not halt the learning of a concept after the bell has rung. Instead, each lesson should enhance previous learning and build stronger conceptual knowledge and deeper understanding among the connectivity of mathematical concepts.

So, now what? I need to find a way to make that connectedness a focus this year. Now that I see the picture this clearly, I have to find a way to structure my lessons to match. Dan Meyer, Andrew Stadel, Robert Kaplinsky, Jo Boaler, I look to you for inspiration and resources. Oh, don’t get me wrong, I have lots of resources already, but I want more.

The problem is I am supposed to be on vacation.  Is it wrong to spend an entire summer vacation fine tuning my professionalism? It is not that I haven’t done summer work before, but so far, every free day I have had; has been filled up with my math passion. As I read, research, and participate in more conversations about math, I find myself unable to slow down. My thirst for additional math and educational knowledge cannot be quenched!

For now, I am going to embrace the passion and curiosity I have for my own profession. Let’s be honest, the moment I really feel like I have a handle on my profession is likely the moment that I don’t belong in it any longer.

Flipping my Teaching, Not Just my Classroom

My teaching approach is getting flipped upside down…repeatedly.

It all started with my on-line introduction to Yeap Ban Har’s discussion on number bonds. Here is the link for anyone interested:  Number Bonds . This was the first time my mathematical mind was blown. Throughout my years teaching elementary school, I had stumbled across multiple approaches in computation, but never had the pitfalls of memorizing procedures and algorithms without context been succinctly explained. This is literally a 2 minute 50 second video!

This one youtube video launched my researching life. Don’t get me wrong, I had always tried to search for great lessons, etc., but this was the first time I felt like I was (for lack of better explanation) doing everything wrong in my teaching.

The timing for this epiphany was not super as I was pregnant with my second child and about to take the majority of the school year off to take care of my baby. In between changing diapers, cleaning spit up, and a very snowy winter trapped in the house, any spare moment was spent investigating better ways to teach math. Fast forward through 10 months massive sleep deprivation, the trials and tribulations (and wonder) of having two children instead of one, and intermittent mathematical research, I was back in my classroom wondering what to change first.

I have written a post about my first foray into 3-act math, as the great Dan Meyer was also a new discovery to me during my maternity leave/initial research period. Not only did I “meet” Dan Meyer, I also was “virtually” introduced to Andrew Stadel, Robert Kaplinksy, Jo Boaler, and of course, the DESMOS and MTBOS communities. Although I have never actually met any of these mathematicians in person, this growing group of educators provides me with daily inspiration.

Throughout this year, many 3 act lessons have made their way into my classroom. One that I recently completed, Robert Kaplinsky’s Zoolander had me questioning if what I was doing was working. Were these lessons as amazing I thought? Did they provide students with a context that made the experience and math meaningful? Were students making connections in their brains? Was I providing enough structure? In short:  effective or not?

zoolander_school_large (1)

Whenever I try something new, it is normal for me to question myself. Acknowledging this fact, I can see that this has been a wonderful transformation for my teaching and math learning for my students. These lessons have had a major impact and I know this from events in the last few weeks. Several weeks after the Starburst lesson by Dan Meyer and the Zoolander lesson by Robert Kaplinsky, my students were referencing them in math conversations in the hallway and classroom. You read that right, the hallway!!! Apparently there was a question on the standardized test about scale models and the students were discussing how easy it was compared to the work they had to do in the Zoolander lesson. Another student commented that the Zoolander lesson helped them really understand the concept better than any book and that was why the question was so easy. I rest my case.

The Starburst lesson initiated a debate about sample space. A passionate debate! When does this happen from a textbook example? I have no reference for that. In short, these lessons make a difference.

Starbursts

At the same time I have felt success achieved in my teaching and by my students, it has also been an immense struggle for me professionally. This is especially poignant with my lower performing students. How do I convince them to believe in themselves and see the beauty in mathematics? If they don’t know the basics, can they still participate in these lessons with confidence? How often will they give the line of, “I don’t understand” in lieu of a rigorous debate with their peers and investigative excitement?

In all honesty, I have experienced both ends of the participation specturm from lower achieving students. Although I had read numerous and convincing articles by Jo Boaler, I only just obtained a copy of her wondrous book Mathematical Mindsets. As I am reading it, I am shouting, “YES! Oh my goodness, I agree! And then in the next minute I am asking, “How can I do this every day? When does procedural math come in to play, does it?” What does this look like lesson by lesson, day by day? Does it transform the students the way she says it does? I am so IN and can’t get enough, period.

As I was researching youcubed, I noticed an opportunity for the summer to attend a workshop with Jo Boaler in California. At this time, I cannot afford to fly to California, pay for the workshop and a hotel room, not to mention the childcare issue, but oh to dream. I am going to take Boaler’s courses through youcubed and finish her book soon. Every free moment I have is spent reading, taking notes, and rereading it. It is my current math bible.Jo Boaler's book

I do not have a neat and tidy way to wrap up this blog post. Once again, I am asking the mathematical world for a conversation about balancing the math classroom. Have you read Jo Boaler’s books? Have you tried 3-act math? What were your successes? What were your failures? How can we work together to keep the math conversation evolving and growing? Anyone else in? Leave a comment, tweet me at @drpolakmath, or send me an e-mail at mpolak@ridgefield.org. The larger our community, the greater our collective success in helping all students achieve in mathematics. Who is with me?

Using Zoolander to Reinforce the Concept of Scale

In search of all great lessons, I stumbled across Robert Kaplinsky’s Zoolander lesson, which was created for the concept of scale.  Although teaching scale was months away when I discovered the Zoolander lesson, I immediately created slides and customized the lesson so that I would not forget about it. I waited for months excitedly anticipating the day I was ready to teach scale to try it out with my students. It looked so good!

For anyone who ever chuckled at the original Zoolander movie as my husband and I did, there is a scene where Will Ferrell’s over the top hilarious character (Mugatu) is trying to convince Ben Stiller’s character, Derek Zoolander, to model for his show. To entice Derek out of his model retirement, Mugatu shows him a scale model of a reading center Derek had previously told his manager he wanted to open for underprivileged children. Mugatu promised Derek that he could open the center if he signed on to model for his show. Derek has no concept of what a scale model is, and when Mugatu shows him the scale model of the reading center, Derek thinks it is supposed to be the actual building. He thinks he is being taken advantage of and claims that the building needs to be at least 3 times as large. Robert Kaplinsky bleeps out “3” in Derek’s retort so students have to determine what Derek said. The question students are presented with is, how many times larger should the builders make the actual school?

Currently, I teach different levels and pacing of algebra. For my advanced students, I gave them very little to go on after presenting the question and the clip. I highlighted some of the math practice standards they were expected to follow such as persevering in problem solving, constructing viable arguments, and reasoning abstractly. I showed them several Zoolander still shots (provided by Robert Kaplinsky), shared the fact that an average story was 10 feet high in a building, and that Ben Stiller was 5’7”. That was literally all the information I gave them. I didn’t know what was going to happen, but I was excited to watch.

Initially, a few students asked for more information, but when I told them that I was not providing them with additional information, they rose to the occasion and demonstrated innovative thinking. My job for the lesson essentially became flipping the still shots back and forth on demand as students worked out strategies. They grabbed my rulers from the class stash and started measuring images on the SmartBoard such as Derek’s arm span and the distance from the building to his head. They started debating whether or not the base counted as a building story or whether the giant book on top did as well. In other words, they persevered and applied mathematical reasoning to an abstract problem because they had no other choice. It stretched their thinking and mathematical prowess.

By the close of the lesson, students successfully shared several strategies with very different answers. (Their answers ranged from 54 times as big to 120 times as big). Some students counted the base of the building and the book and others didn’t. A few students compared the model people to the height of one floor and made their mathematical predictions based on that relationship. Several people concluded that there were about 12-13 stories and used the other information to make their calculations for the scale factor. Students also estimated that based on Ben Stiller’s height, the model was about 1.5 feet and made their calculations from that vantage point. What all students were doing, regardless of whether or not they knew how to get to an answer, demonstrated an understanding of the scale factor and scale model concept based on their problem solving application. One student asked me, why are we doing this? As I repeated the question back to him, he rolled his eyes, smiled, and said, “To apply the scale model concept to something beyond the math book.”  Ha! Nailed it!

I then decided to try the same lesson with my other classes, but I knew they would need additional scaffolding. Based on my observation of the advanced students, I inserted additional clues in my slide presentation. Before I showed them the stills and provided Ben Stiller’s height and the average height of a story in a building, I structured the lesson like a Dan Meyer 3-act lesson. After showing them the clip of Zoolander with the scale model, I asked students to write down any questions that came to mind. We shared with each other. Some questions were, how tall is Ben Stiller, how many feet was the model, how many students are supposed to attend the school, what will the budget be for the school, etc. At this time, I let students know that their task was to determine how many times larger the actual school had to be in relation to the scale model. I asked students to come up with a wish list (if I would grant them their desires) of tools and/or information to help them solve this problem. Students asked for the answer (naturally), the height of the model, how tall a story was, the size of the plot of land for the building, and so forth.

Disappointing, but not surprising to them, I provided them with the limited information I had provided my previous class. This included the height of Ben Stiller, the average height of a story in a building, and several still shots from the video clip. I offered them rulers (which was the one change from the other class who just asked for them) and left them with a final thought before giving them time to solve:  Now that you know your task and the limited tools you will be provided, what strategies could you use to unravel this mathematical mystery? How can you work around not having the exact information you want?

Many students who tend to struggle rose to the occasion and illustrated bravery in taking chances in solving the problem. Yet, students who tend to crave procedure and rules were taken aback (as has been a pattern for them with these types of lessons) and continually asked me for assistance. With every question these students asked, I responded with another question. The uneasiness some students experience when not knowing exactly what to do has proven to be almost debilitating.  That makes it my job to make these students feel uncomfortably comfortable. I can’t just give them answers; I have to provide them with tools to independently and confidently find ways to chase the unknowns in math. This is an ongoing challenge for me personally and I am always searching for ways to help students help themselves.

Overall, the conclusion of the lesson resulted in a very similar outcome when compared with the advanced class closure. However, I made another change for this class and used the third act. The third act was sharing the Zoolander clip (previously bleeped by Kaplinsky) where Derek says that the building has to be at least three times as big. The class laughed and commented on Derek’s terrible analysis. A few savvy students reflected, “Well, technically, he isn’t wrong. He said at least 3 times bigger.”

I was on the fence after I used this lesson as to whether or not the process helped students strengthen their understanding of the scale model concept for all levels. For the advanced students and many students in my other levels, I certainly think it did, but perhaps I am justifying a fun experience in my room. Some lessons are like that. Yes, they make a class enjoyable, and yes, they seem like they are mathematically sound, but in the end, as a teacher, you can’t help but question if the lasting impact of the concept was made. I never forget that there is more to a math lesson than being “Really, really, ridiculously good looking.”zoolander_school_large (1).jpg