5 Things to Jumpstart PBL in the New Year [Math Version]

@amyshamblen

   You've enjoyed the holidays and you have a few more days until school starts back up so you've been catching up on your reading. Several of your friends have gone to trainings during 2018 where they have learned about Project Based Learning and you are intrigued. But everything you have read gives you a headache because you couldn't possibly add anything to your full curriculum pacing guide. 

   This post is for you. And it's for anyone who wants to "just kick the ball down the PBL road." Where do you begin? How do you get started? Well, in my opinion, it should start with inquiry. 

    (1) Start every (yes, every) day with an opportunity for your students to ask questions of you and of each other around the topic of math. It does NOT have to be about the current thing you are doing in your math unit. As a matter of fact those who espouse spiraling in topics throughout the year would argue that you should choose things that are not in your current unit. And, it is ok to give a problem that you haven't covered yet. Let your students struggle with figuring out the answer and then let them know that they will be seeing many more problems like that in a few weeks. 

  Want a question to start it off? Look at the image at the top of the page.  Ask you students to estimate the number of total balls that were in the glass. Then ask them to estimate the volume of the glass. And, finally, have them estimate the volume taken up by the balls when they are all in the glass. An "extra credit" might be how many more balls could you add to the glass until it is full?  Notice there weren't any numbers given. There weren't any formulas given. Just tell them that there isn't a correct answer but there are an infinite amount of incorrect answers - those that came without sound reasoning. 

    (2) Encourage your students to reflect on what they already know and what they will need to know to be successful in the next unit. Start by going to the Extended Questions or Gifted and Talented Questions at the end of the chapter you are about to begin. Find a question that you can bring to life and assign it on the first day of the chapter. If you don't have something like that then explore online resources for questions about the topic you are about to cover and select a rich question. Make sure the question can not be solved on the first day by the majority of your students. Once you have shown the question to the class, ask them to come up with what information they need to know to be able to solve it. List these on the board. Check those items that the students have not yet covered. Explain to the students that these checked items will be what you will be teaching them in this unit. 

    (3) Give your students opportunities to discuss how to solve problems in groups. Give them problems that might have multiple ways of solving. Allow time for everyone to attempt the problems. Then have them form groups and take turns explaining how to solve the problems. Encourage multiple ways of solving by asking them to come up, as a group, with more than one way to get to the solution. Teach the students how to give constructive feedback for problems that are incorrectly solved. 

    (4) Find ways to have students present their ideas to the rest of the class. (a) Start safely by using a fishbowl where a group discusses solutions in their group while the rest of the class observes and takes notes on the discussion. Just make sure the observers are held responsible for giving constructive feedback to the group in the fishbowl. (b) Have students paired up (Pilot/Co-Pilot) with the understanding that each day will change whether it is the pilot or the co-pilot who is responsible for explaining solutions. When working with your lower groups you can have it that either can answer but the selected position must tell the other person if he or she isn't going to be directly answering. 

(c) Have a presentation day where students write their solutions on poster paper or on a white board. Then have a gallery walk where students give constructive criticism to their peers. 

   (5) Put it all together. (a)Give an assignment over a topic that has not been covered. (b) Create a knows and need-to-knows list that students generate about the assignment. (c) Give students opportunities to work in groups to find solutions to the the assignment. (d) Have opportunities for students to share what they know with others in the classroom. Include an end of chapter/unit day when the solutions are "officially" presented. 

    What I have just shown you (paragraph 5 above) is the basic structure of project based learning.  If you committed, today, to doing this for each of the units/chapters you have left for this school year then you and your students would benefit from the deeper learning that would occur. 

    Then, next Summer (after an incredible Spring), you would want to commit to continuing this process in the Fall semester. When you planned for the Fall you would look for a math topic that is related to a news item or other item of interest in your local community. You would, then, find a way to connect with someone involved with the community issue. Then you would figure an angle for your students to do some math to help solve the problem (or, as a minimum, have them find several possible solutions to the problem). Finally, you would make sure you have a presentation day that your students would be tasked with presenting their solutions to the community. That one problem would demonstrate what true PBL is all about. It would have a "real world problem," it would have inquiry, it would have collaborative work and discussion, it would have reflection and analysis, and there would be a public audience. 

     It is my belief that students need three things to help them go deeper in their learning: Something that makes them wonder; time to discuss what it is that they are wondering about; and a non-negotiable deadline where they have to tell someone, they don't know, all about this thing that they have been wondering about. 

Photo by Annie Spratt on Unsplash

     Following these steps will help your Spring semester be the best you've ever had. Isn't that what all teachers should wish for on this New Year's Eve?  Happy New Year and best of luck in the coming semester. 

Some books to help you on this journey: 

Jo Boaler's Mathematical Mindsets is just plain good reading. 

Geoff Krall's Necessary Conditions is about great math teaching.

My book, Project Based Learning in the Math Classroom, (co-authored with Telannia Norfar) will help you go deeper with what I have written in this post. This book is now available for pre-sale and will be out in April 2019. 

Fix Those Problems (Math Teaching 101)

http://wronghands1.files.wordpress.com/2013/06/math-problem.jpg

First, and foremost, I am a student of instruction.  My resume says I have taught math from 6th grade to college algebra; I taught middle school science; I taught introduction to engineering design and digital electronics at the high school level. And, I facilitate teachers in using project based and problem based instruction (PBL).

What I enjoy most is reflecting on my practice and pursuing better ways to perfect instruction in the classroom.

During the last 6 years I have tried to figure out how to best teach mathematics in a PBL environment. As a practitioner I tried differing ways of providing inquiry while including repeated practice. Then I was introduced to problem based instruction where the depth of inquiry was constrained so that the time frame could be reduced from the normal project length. This worked better in math, for me, and yet I have seen teachers who were still able to keep the longer project settings.

In recent years I have been working as an instructional coach and I have started working for the Buck Institute for Education, BIE. Through these I have been able to offer ideas to many math teachers and I have listened to their concerns.  The common thread between these teachers is the difficulty of following the guidelines for project based instruction while dealing with students who have math skills that are as many as 5 years lower than the class they are sitting in. This is true whether they were teaching in California or Maine.

In Texas we now have state exams that are "more rigorous" (gag me - hate that word, rigor) and with the common core (CCSS) standards you are expected to think logically and to demonstrate concepts. No longer do we just show basic mathematical manipulation of numbers. We expect that students will read a scenario and then apply mathematics to reach a conclusion about a numerical relationship.

Teachers keep asking me to give them good examples of problems with the "proper rigor" (there's that word again). My answer is that all you have to do is look at any, yes ANY, math problem in any math book and take the root problem and embellish it.  The following is an example from a Glencoe Pre-Algebra book. I took it from the 5th chapter and it is question 5 from the chapter test: "Trish bought a CD player for $37.58. The price she paid included a discount of $6.63. How much did the CD player cost before the discount?"

Now let's make it better and bring it up to 2014: "Trish wanted to buy a used iPhone at Best Buy and had saved $50 to buy it.  She searched online for savings coupons and found 3 that said they were the "best buy at Best Buy." The first was for $6.63 off of any used phone marked $40 or less. The second was for 15% off of any used phone costing more than $30. And the last was for "any phone in stock" and was for 12.5% off of the list price.  Which coupon should she use so that she spends less than her $50. Explain to her why she should choose that one. Also assume there is a 6% sales tax in this state that will be applied to the final cost."

In this problem students still need to look at percent increase and percent decrease, which was the main skill being tested in problem 5. But now they have to do some thinking. And, if you let them work in pairs they can have discussions about which is the best answer. That took me about 10 minutes to get it into the post. I looked at problems on the Glencoe website, picked the problem, and then I upgraded it.

What if you did that with one problem every day? What if every summative assessment had problems like that and your students could work in pairs to get the right answer - but each person had to write the correct answer and the reasoning of why it is correct? Need another example? Here you go...

"You are carpeting a rectangular room that is 3.5 yards by 4.5 yards. The carpet costs $15 per square yard. How much will it cost to carpet the room?" This is from Big Ideas Math. Now let's make it better.

"Mr. Smith wants to put carpet down inside of the doors that lead out to the playground so students can wipe their feet when they come in. He wants the area covered to be rectangular and be as wide as the doorway but extend at least 3 yards into the room.  Explore 3 stores for prices of carpet and determine how much it will cost to buy the needed carpet. If you can not measure the width of the doorway assume that it is exactly 2.5 yards wide. Be ready to explain to Mr. Smith which store has the best price and why it is the best price"

It's time to take back your classrooms. Give your students opportunities to work together and analyze situations. The infamous "they" want your students working on rigorous math problems. You have math problems all over the place! Use them, improve them, and then let your students get to work on them. It's not rocket science - but with the right guidance your students might just become rocket scientists.

Loving What I See At Our School

Today I was able to get into a few of our math classes. I started with two of our 6th grade classes. Since they plan with me and we all plan together, I knew that they would be teaching the exact same concept but we really push the idea that every teacher is their own person and can teach in whatever way they feel comfortable.

The concept: Finding Greatest Common Factors and Least Common Multiples with Venn Diagrams

In the first room our teacher was starting with a video rap about multiples. His surround sound system with max base had the class rocking. Then he projected a blank venn diagram and asked for students to explain how a venn diagram worked. With this still projected he brought up a video explanation with the video venn right where the other had been.

The students, meanwhile, were taking notes and following along with the videos that were embedded in our LMS (Learning Management System) called ECHO.  When I left, the students were engaged and actively working on this:

Across the hall I went to the other classroom where I found the teacher engaged in an explanation of accessing something on the iPad - in Spanish. We are happy to have many bilingual teachers in 6th grade and with dozens of students who have Spanish as their primary language, it sure helps.

As I entered the room I couldn't help but notice that the activity (above) was up on the board.  The students had their iPads open and were busy working.  As I scanned the room I noticed some QR codes on a board for each period with "Answers to Friday's Quiz" written about them. Since I was in 3rd period I scanned the 3rd period QR and it took me to a Padlet that was blank.

The teacher told me I should scan the ones for 1st and 2nd since they had worked on this and so I scanned the QR's.  There I found students had placed the problems from the quiz that they had worked out using Educreations.

Two different classes. Two different teachers. But the same content. Both classes were steeped in technology use but were using different apps and/or sites. I went to these classes randomly and I left feeling really good about the math instruction our 6th graders are getting. A teacher, new to the school, asked me as I walked back to my office, "Would you have your kids at this school?"  That's a resounding YES!

Thoughts on Co-Teaching a Class

At our school this year we are experimenting with ways to improve the educational experience of our math students. This experiment deals with two math teachers teaching the subjects of Algebra and Geometry to the same group of 9th graders. The students, as of right now, will stay with these two teachers until they have completed the state mandated mathematics objectives for both subjects. The hope, and expectation, placed on this experiment is a deeper understanding of the foundational math skills required of all students taking 4 years of mathematics in high school. This will, in turn, improve the results of our students when they take the state mandated tests at the end of the year.

What I haven't told you is that this experiment is going on in my classroom and my co-teacher and I are the teachers mentioned above. So, we have completed almost three weeks of school and here are my early observations:

1. Planning is now something that is done with two perspectives. That may sound obvious but how many times have you said, "oh, I forgot about that." Now, one of us is bound to have thought through a particular angle that might have been missed by a single teacher. Also, I am finding that we are able to plan much farther out in the calendar. We will get together, for example, tomorrow and go through the basic nuts and bolts for the next three weeks of our second project while evaluating the end of our first project which wraps up this coming week.

2. Grading can now be done more expeditiously. As a matter of fact we are finding that I really like grading tests and quizzes (which is a very long process because I go through every problem for every student to see their work and evaluate their thought process), and my co-teacher doesn't mind doing the daily homework, classwork grading (things I hate to do and which would always end up piling up on my desk). This may change after a while, but for now, I think we're both happy.

3. We are starting to have an almost husband/wife relationship in front of the students. What I mean by this is that we play off each other's thoughts, we do the whole "good cop/bad cop" thing, and we feel comfortable poking fun at each other. This has led to times when one of us is not feeling like dealing with a certain situation in class and the other naturally steps in to take control of the task at hand. We have also caught students asking one of us for permission, not getting it, and then coming over and asking the other one of us for permission; a classic child/parent scenario.

4. Our pairing is especially good because of our age, and experience, difference. My co-teacher is in her 2nd full year as a teacher, is working on her Master's in Math Education, and is recognized by our district and the University of Texas' UTEACH program as an exceptionally gifted teacher. I've been teaching since 1992 and have taught in a variety of situations. Her hard driving, go-get-em approach is nicely tempered with my even-handed, seasoned approach to teaching. Between the two of us we are able to find a sensible middle ground in all that we do.

Working with another teacher in "your classroom" can be a bit disconcerting, at first. There needs to be a willingness by both teachers to collaborate on all decisions. As with all good teams, egos must be put aside so that progress can happen. Because, the progress we are really talking about is the progress of our students. The state, superintendent, principal, and parents don't care which teacher does what in the classroom as long as the students are successful. And, that is what we are seeing in OUR classroom. Learning is happening and I'm excited about the possibilities.