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.

Exploring Design Thinking as a PBL Guy

Via Eric White

This week I will be meeting with other BIE National Faculty (NF) members at our annual Spring Summit.

For the summit we have broken into Professional Learning Communities (PLC's) and I am with the Design Thinking (dt) group.

We will be sharing with the other NF and we are looking at how dt compares with pbl and what can and should be included in future editions of the BIE PBL 101 or other training services.

I have been thinking a lot about the dt world and I have both watched from afar and interacted directly in the Twitter chat on dt - #dtk12chat. I have sat through a number of presentations from key people in the dt world including Ewan McIntosh. I also have a masters in engineering science so I've taken a few courses in design.

But I still haven't totally been able to marry dt and pbl. As I talk with more and more people who subscribe to dt I am noticing that many of them will do projects using the standard pbl process and then do another project that is based upon the dt process. I am assuming that I'm not the only one with this struggle.

During my years teaching with Project Lead the Way I used the 12-step design process with my students. Since I was at a New Tech Network (NTN) school I was able to marry the pbl process with this process and I worked my projects with the marriage of these two processes.

Project Lead the Way (PLTW) Image

Overlapping the DT image at the top of this post with this design process I came to the following list of steps for a pbl project with an undercurrent of dt:

1.     Initial Problem or Idea                    
2.   Brainstorm and Build Empathy  
3.     Consider Criteria and Constraints
4.    Create an Initial Concept (IC)       
5.    Gather Feedback on the IC            
6.    Create an Initial Prototype (IP)    
7.   Gather Feedback on the IP           
8.   Create/Build/Write/Make           
9.    Mid-Creation Feedback                 
10.  Present Final Product (FP)         
11.  Gather Feedback on FP               
12. Reflect                                            

This is a 12-step process that starts with a problem or idea, overtly asks teachers to think about inquiry and empathy, gives opportunities for feedback, has a presentation, and ensures reflection.  

Looking at another interpretation of the phases of the design thinking process we see that within this 12-step process there is empathy; there is a chance to define and ideate; there is an opportunity to create a prototype; and there is a chance to test the prototype and get feedback.  

As we at BIE attempt to create the essential elements of "Gold Standard PBL," we are looking at these elements:

http://www.bloomboard.com/

The 12-step process I presented can, and should, contain all of the elements in this diagram. As with all learning we must make sure there are key knowledge and skills at the heart of whatever process we are using. 

If we can ensure students are involved in their learning, are thinking of others, and are reflective in their quest for understanding, then our students will be the kind of adults that make a difference in our world.

 

It's Time For a Project

 

https://www.flickr.com/photos/dullhunk/

It's that time of year again for many (most?) of us in the K-12 world of the United States to deal with standardized testing.

And there are many teachers who have been waiting until "that test is over" to start a pbl project.

There are some of you who can't see past the test that is approaching. I understand. But post-test can be the perfect time to knock out a project. And, therefore, now is the perfect time to start planning for that project that will put you and your students on the WOW end of the spectrum. You can do it and there are many of us out here willing to help you on your path forward.

So where do you start with the planning? Content, content, content. What things did you want your students to learn this year? Is there something that you know your students didn't learn at the requisite level? Maybe there's something that they were supposed to learn that you or the students really enjoyed and the topic is perfect for going deeper in their learning? Maybe there is something that they will need to know for the next school year and you might want them to explore it now?

If you are looking for project ideas I have two places you can go, right now, to see projects that might spark you imagination.

First place, of course I'm a little biased, is the BIE website. Look under the Resources Tab and you will see this:

In the Project Search area you can find hundreds of projects that teachers have uploaded. Although I tell teachers to NEVER use a project exactly as written, there is nothing wrong in looking over a project to whet your appetite. While you are in the Resources Tab, go to the Project Planner and do all of your planning in one place.

If you need more ideas for projects I always recommend High Tech High . Their list of projects (under the Project Tab, of course) is quite extensive.

Project planning can be a chore and, if you are new to pbl, it can be somewhat daunting. Don't do it alone. Enlist your fellow content teachers or a friend to help with brainstorming project ideas. And, even better, ask your district or school literacy coaches, instructional coaches, or curriculum specialists to help.

To be successful, you MUST take the time, up front, to get every day mapped out. Only then will you be able to feel comfortable and confident with the daily flow within you classroom. And, only then, will you have the time to work closely with individual groups of students.

When your students present what they have accomplished to a group of professionals and they are answering questions and engaging in conversations with these professionals, that time you spent up front will seem like nothing. But you will be everything to your students.

Another Take on Problem Based Learning for Math

https://www.flickr.com/photos/gpforeducation/

I have been wrestling with the marriage of Project Based Learning (PBL) and Math for nearly 8 years now.  A few years ago I moved towards Problem Based Learning (PrBL) instead of Project Based for math. It just seemed to make more sense.

With PrBL there are shorter time periods to complete a problem which, to a math teacher, frees up more time for "Math Skills." Of course a veteran math teacher, using inquiry-based teaching (PBL or PrBL fall into this niche), will find opportunities for practicing math skills.

Once a teacher decides to pursue PrBL, he or she will need to figure out which math units fit best. Or at least that is what I used to think. Now, after years of working with this, I realize that instead of figuring out which units and then what specific problems to work with, there is a better way.  Teachers need to start the planning process with great "Open-Ended Questions."

Now I use the term "open-ended" loosely because many of the problems I found with that label were actually closed problems.  The open-ended problems I am looking for may have multiple solutions but they may just have multiple paths that can be taken to get to an appropriate solution.

So here's a problem I found for middle school students (taken from the Math Forum):

I can see this being used as an introduction to area. During the first day's questioning I would hope there would be obvious questions about how to calculate area. But I would also hope to hear questions about whether the "whole number dimensions" have to be in feet. Could they be in "whole" inches? How about a question about whether "rectangular" means it has to be four sided - could it be a composite figure of rectangles? There might be a question that comes up that I would never think of.

The beauty of this is that the students can explore their specific questions to solve the problem going down a path of their choosing. At the end of the week the real question is: "Can the students solve a 4-sided, rectangular figure, with a length of L and a width of W?"

My big AHA! then was this - what if I found 20 or 30 or 50 great open-ended questions that represent content I want my students to learn during a school year?  I could then lay these questions alongside my district Year at a Glance or Pacing Guide to see where the questions would make sense on the calendar.

Now as a teacher gets to each unit they will already have 2 or 3 (or 5) open-ended questions that have been vetted. These will be the problems used in class to foster inquiry.  These problems will take 3 or 4 days from start to finish. There will be opportunities for questioning and brainstorming; creating drawings or other models; presentations; and reflections.

For example, the questioning and brainstorming might be completed on the first day. The modeling (along with the requisite critical thinking) might be on day two. On the third day there would be an opportunity for an informal presentation of how the groups solved their problems, followed by a reflection. On the last day of this PrBL there might be an assessment on the learning that was completed.

This all started from having a sound, content specific, question that fueled inquiry, questioning, and thinking. Using an open-ended question allowed students to go in different directions in pursuit of answers. Successful students ask questions, think critically, and defend their ideas. That is where deeper learning happens and that is how we help our students develop perseverance.