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. 

The Learning Process Must Include Inquiry

http://bit.ly/2pPDPQh

Today I worked with a teacher planning a unit and I realized that the idea that we need to kick start the inquiry process on Day 1 of a unit isn't obvious to every teacher. The following post wrote itself as I walked her through the process of making inquiry the foundation of all that she does moving forward.

Whether you are a veteran teacher who has taught each of your units multiple times, or you are a novice teacher wanting your students to be more involved in their learning, adding inquiry processes to your teaching habits will help your students go deeper with their learning.

Michael McDowell (@mmcdowell13 on Twitter) in his book Rigorous PBL by Design emphasizes that inquiry not only helps on a daily basis with student knowledge but can help identify student performance. He recommends that teachers continually find answers, from their students, on these 4 questions: (1) Where am I going in my learning? (2) Where am I now in my learning? (3) What next steps am I going to take in my learning? And, (4) How do I improve my learning and that of others?

As I became a  New Tech Network (NTN) teacher, 10 years ago, I was instructed to gather a similar list of information using the structure "Knows and Need To Knows"(KNTK List). The list was displayed in a two column table with all of the things the students already knew that could help them learn on the left, and all of the things the students needed to learn to be successful, on the right. Since McDowell was intimately involved in the NTN for years it makes sense that his four questions have a range similar to the extremes of "Knows" on one end (Where am I now in my learning) to "Need to knows" (What next steps...and...How do I improve...).

For the last 6 years I have been a National Faculty (NF) member with the Buck Institute for Education (BIE.org). BIE and the NTN were intertwined for years and their philosophies were very much the same. And so, as I began with BIE, we trained teachers to use the Knows and Need to Knows (KNTK List) format for helping students see where they were in their learning and where they would be going in the learning process.

As I worked on perfecting my own inquiry practice I ran across a book that would, forever, change how I approached inquiry. It is called Make Just One Change  by the Right Question Institute (@rightquestion on Twitter). This book teaches you the Question Formulation Technique (QFT). In this technique students are asked to brainstorm a list of their personal questions about a topic that is being introduced. They then get together in groups and refine their questions creating a list of 3 questions that are their most important questions as a group. Finally the class creates a list of questions based upon the 3 questions from each group. This list is now the Class List of pertinent questions.

Ironically, within a few months of reading the book, BIE announced that the NF would be replacing the KNTK List with the QFT process in the PBL 101 trainings. Needless to say I was ecstatic with this change.

The three processes mentioned are at three levels of comfort for the teacher in the inquiry process, in my opinion. If you are new to an emphasis on inquiry then start simple and start creating a KNTK List. On the first day of a unit give the class an overview of what needs to be completed in the unit or give them a challenge or some product that must be completed by the end of the unit. Then have them generate a list of all of the things they already know how to do and that they will need in the unit to be successful. This is their "Knows." Then have them brainstorm things that they will need to know to be successful. This list will complete the KNTK List.

If you are more comfortable with your teaching then it is worth your while to get a copy of the QFT book so that you can see the QFT explained in its entirety. As in the paragraph above, you start with something that stimulates the inquiry process. The students, individually, write a list of questions that come to mind from this prompt. After a set time, the students get together in groups and share their questions. The groups select three questions that represent the group as a whole and, finally, the groups share out the questions making a Class List of questions.

The Four Questions, described by McDowell, is the next level and requires you to assess the students on the questions each day so that you are able to enhance the overall learning in the classroom. This is the where I am heading with my own inquiry process in my classroom. It takes some work but with the guidance in his book, you can make the changes necessary to help yourself become a more effective teacher and to help your students make better connections with their learning.

There is still one key element to successfully having an inquiry based classroom. No matter which process you use it is imperative that you make time each day to explore the KNTK List, Class List of Questions, or the documentation for each student through McDowell's approach. Every day you need to make this a part of your classroom routine. Most successful teachers I know use the last 5 to 10 minutes to interact with the lists so that the students can do one (or both) of two things: Line through or check items that have been addressed satisfactorily AND add items not already on the list that have come up in discussion during class. These lists are fluid and give the class a visual of their learning.

It isn't too early to become a better teacher and improving questioning and inquiry will help you improve and will increase the depth of knowledge attained by your students.