Problem-based learning (PBL), also called project-based learning, is a great way to motivate learners and address those core competencies and big ideas presented in BC’s new curriculum (if you aren’t familiar with BC’s new curriculum, there’s an increased focus on cross-curricular competencies, including critical and creative thinking, communication, and personal and social competency). Students solve real-world problems, often collaboratively, and usually integrating outcomes from multiple subjects.

** 1. Start Small**

Great PBL problems often take students several weeks to question, research, collaborate, design, iterate, and share. They often integrate outcomes from multiple subject areas. However, PBL can also take place in a single lesson within a single subject. I’m planning on starting with a few simple ill-structured problems in math to get my students (and myself) comfortable with the process and work on developing those communication, collaboration, and critical/creative thinking skills before embarking on anything larger.

**2. Start Local**

Are your students going to solve nation-wide on their first try? Probably not. Something in your immediate environment is a better starting place, so I’m going to start by picking an opportunity in the classroom or school. Maybe students can design a new room arrangement to provide better collaborative learning spaces or access to resources such as the library. Or, maybe students need to come up with a method to limit waste in the classroom or school.

**3. Set Specific Time Goals**

How long will students have to brainstorm? Research? Share with other groups? Re-assess their ideas? Share out their learning at the end? Communicate these timings with students right away to keep them focused on the goal. This will set them up for bigger projects where it’s easy to lose track of the end goal and drag on.

**4. Purposeful Groupings**

Don’t randomly group students! If there is a lot of reading required for the project, make sure there are strong readers in the group. Consider assigning roles in the group- leader, reporter, etc. One article even suggested grouping students who seem to ‘ride the coat tails’ of other students together to make sure everyone is contributing. Have students debrief on their contributions and reflect on how to collaborate better.

**5. The Product is Important, but not the Focus**

It’s important to share with learning how their learning should be presented- are they pitching their idea, creating a product, sharing out orally to the class, making a poster? Who is their audience? However, it’s important that the main event is the time spent brainstorming, researching, and collaborating. Hours spent on a beautifully decorated poster may be better spent building those core competencies through brainstorming, testing, and refining ideas.

**Have you used PBL in the classroom? What are your tips for beginners? Things that worked, or things to avoid?**

**Two Great Articles to Learn More:**

*Education World’s *Problem-Based Learning: Tips and Project Ideas

*Edutopia’s *Twenty Tips for Managing Project-Based Learning

**A bit longer of a read for math (with some great ideas for each elem. grade level):**

Problem-Based Learning in Mathematics: A Tool for Developing Students’ Conceptual Knowledge

(Literacy and Numeracy Secretariat, Ontario Association of Deans of Education)

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Today I’m sharing one of my favourite books for teaching math- this is Marian Small’s “Good Questions- Great ways to differentiate mathematics instruction. This book has really helped me wrap my head around how to differentiate instruction and teach around BIG IDEAS, which is a major component of BC’s new elementary curriculum. BC Ed Plan is asking teachers and students to “personalize learning” and make outcomes accessible to students of all abilities, and this book is designed to do just that. Marian Small is an amazing mathematics educator and professor, and so this book is perfect for anyone looking to design lessons that foster number sense and deep understanding of math concepts that are accessible to all students.

The book focuses on two strategies for differentiating instruction based on big ideas- these are open questions, and parallel tasks. I’ve found both these strategies to be hugely helpful for getting all my students engaged in math, and they were really easy to implement, so I’d recommend them both to all math teachers.

Open questions are questions or problems that can be accessed in a variety of ways- they are going to have a range of correct answers. Below is one of the examples she gives of an open and closed problem- the first problem is only really accessible if you understand what a fact family is, but the second can be answered in a variety of simpler or more complex ways. This way all students can be part of the conversation and be successful.

As well, when students share their solutions in a group or as a class, they can benefit from talking through and listening to their peer’s ways of thinking, which can help students understand more complex ways of thinking in math. The book goes over several ways really easy ways to create open problems or adapt them from closed problems from textbooks or worksheets you already have.

The second is parallel tasks, which is where a teacher creates two or more options that focus on the same concept. However, there might be a simpler and more complex option, or a 2D and 3D problem, or a symbolic and pictoral option. All students can talk about strategies they used to solve the problem, regardless of what option they chose, and are all working towards the same big idea.

The book breaks down big ideas in Number and Operations, Algebra, Geometry, Measurement, and Data Analysis and Probability for Pre-K to grade 2, 3-5, and grades 6-8. With each big idea she presents examples of open problems and parallel tasks and explains how to design, implement, and assess these problems.

**My big takeaway: **we need to slow down, let kids explore deeper into problems, solve them in multiple ways, and share their learning with their peers. And as much as possible, problems need to be accessible and appropriately challenging to all our students.

This is my absolute favourite book for personalizing learning in math and reshaping my teaching around the new curriculum. I hope you check it out! I’d love to hear in the comments what resources you’ve found that are great for personalizing learning and addressing the new curriculum!

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I was inspired this week by Dan Meyer’s TEDtalk entitled “Math Class Needs a Makeover” in which he shows how he takes a typical textbook question and reworks it to stretch student thinking and make math relevant and accessible.

I wanted to see if I could do the same with an elementary textbook question, but my approach had to be a bit different because:

a) Dan Meyer has tons of experience doing this, and this is my first attempt at PBL in math.

b) Elementary textbooks don’t tend to include the same multi-step problems that high school textbooks do, making them a bit harder to break down.

I decided on choosing a shorter problem to build upon and try to transform it into a problem-based learning jumping point. I used Math Makes Sense 5, as this textbook is frequently used in the classrooms I’ve taught in. As it’s spring break, this week is just a brainstorm, and I’m hoping to test some of my ideas out in the classroom in the spring.

**Sample Math Makes Sense Problems (Pg 196): **

A

ferry leaves Port Hardy at 07:30 and arrives in Prince Rupert at 22:45. How long is the journey?

An overnight ferry leaves Shearwater at 23:45 and arrives in Port Hardy at 08:10. How long is the journey?(Morrow, P., Connelly, R., Appel, R., Chichak, D., Keyes, B., Johnston, J.,… Jeroski, J. (2005).

Math makes sense 5.Pearson Education Canada.)

**New Curriculum Connections in Grades 4 and 5:**

Curricular Competency:

- Engage in problem-solving experiences that are connected to place, story, and cultural practices relevant to the
**local community**(4, 5)

Content:

- How to tell time with analog and digital clocks, including 12- and 24-hour clocks (4)
- Duration, using measurement of time (5)
- Number concepts to 1000000, Multiplication and division to three digits (5)

The original problems were simple 24 hr conversion, adding on/subtraction questions. However, if you actually look at the BC Ferries schedule, it doesn’t actually use 24-hour time. Not saying you couldn’t still use this as a jumping point for exploring 24-hour clocks if students were asked to convert for a purpose, but the problems as they are in Math Makes Sense don’t really connect with how students may interact with ferry schedules outside of school.

So, how can ferry schedules be used to spark a PBL math lesson, or project?

**Some ideas:**

- You’re in charge of designing a new ferry schedule from Salt Spring Island (Fulford Harbour) to Victoria (Swartz Bay) to replace the current ferry, the Skeena Queen
- What size of boat should you use?- capacity, cars vs. walk-ons…
- When will the ferries run (could be in 12-, 24-hour clock, or both)

- You need to get from one of the Southern Gulf Islands to Vancouver. Should you take the ferry through Swartz Bay, or a Gulf Island ferry?- much simpler of a problem, but not as clear cut if you look at different times, time vs. cost, ease of travel…
- Your group is in charge of proposing a new ferry route (possibly the rumoured downtown Victoria-Vancouver route) . Your group needs to come up with a timetable using the 24-hour clock and choose what size of ferry (how many cars/passengers can travel each trip) the route will use.

Stay tuned for an updated post of how this works in the classroom!

**What are some other opportunities for place-based math on the West Coast? What have you tried in your classroom? Or local connections to other places? Feedback? I would love to hear your thoughts in the comments!**