Lessons We Can Learn from the Early Years

I was just reading an Early Years resource called Thinking Mathematically, published by ETFO as part of the Thinking it Through professional learning package. I came across this quote and wondered why it is only suggested for young children. Shouldn’t all mathematics experiences follow this integrated idea? Here is the quote:

“Mathematics for young children should be an integrated whole. Connections between topics, between mathematics and other subjects, and between mathematics and everyday life should permeate children’s mathematical experiences.” p.7

The authors continue to discuss the importance of mathematics activities occurring in the context of an experience; a real purpose or connection to doing the math. I believe students at all ages would benefit from this type of math teaching and learning experience. The authors also talk about establishing a ‘climate of delight’ in the classroom and I can see how this works with older students as well.

I have had the chance to work in several Intermediate math classes recently who were studying proportional reasoning (not the easiest of concepts for students!). What was interesting to me was the level of engagement in the classes when they were engaged in some problem solving activities where the teachers incorporated student interest, choice, real-world connections and 21st Century skills. Some students created their own math problems using any real scenario possible in an area of interest to them, some used Tim Horton’s cups to try and find out what the best deals are for different sized drinks, and some chose objects of interest in their own lives to determine if a proportional relationship exists (e.g. are the screen size and case size of a smartphone and tablet proportional). In all of these lessons, students used iPad apps of their choice to create online tutorials. In these classes, students had learned four specific strategies for solving proportional reasoning problems: Unit Rate, Factor of Change, Fractions, Cross-Product Algorithm. The tutorials were designed to teach someone else how to apply the proportional reasoning problem solving strategies.

As we wind up this school year, I hope we can take a page from the Early Years classes and find some exciting ways for students to apply the math they learned this year in a fun and engaging problem of meaning to them. If you have had any experiences like this, or ideas for things to try, I would love to hear about them!

Using a Wiki in Math Class

This summer, I created a wiki that teachers could use to engage students with creating  online content in Mathematics. The idea was to improve mathematics achievement by engaging students in collaboration, communication and vocabulary development using 21st century learning tools. The idea was inspired by an NCTM workshop called The Mathematician’s Notebook by Tammy Jones: http://www.tljconsultinggroup.com/nctm-2012-annual-meeting-exposition-philadelphia-pa and by research into literacy/mathematics connections and educational technology use in mathematics.

I am posting the framework here for educators to explore, copy, re-mix and adapt to use any parts of it with their own students. The samples of student work are all created by me as examples of what students might create. If you do use any of the pages from here, I would love to get feedback from you and/or your  students about how the wiki is being used.

Enjoy visiting the Mathematician’s Notebook wiki!

iPads in the Math Classroom

Several of our schools have been participating in a Collaborative Inquiry project involving iPads in the Math Classroom. We have classes using the iPads along with the TIPS4RM resource. One of the inquiry questions was about the impact of using technology and the TIPS4RM lessons on student engagement. One of the ideas being tried is to simulate an IWB lesson without needing the classroom space for an IWB. Teachers connect a projector to their laptop and use an app on their iPad called Splashtop streamer to control the computer. Teachers or students can use the iPad to show their work during class without having to maneuver around the room. How is your school using technology in math class? We would love to hear what else teachers are trying and how the students are responding!

TIPS4RM is Taking the Stage

Andrea and I were thrilled to hear from several teachers who are taking a leap of faith and moving toward using  TIPS4RM as their core resource this year. For the past couple of years, Intermediate teachers in the Greater Essex Board have been learning about this resource and using it to supplement their textbook lessons. One issue with that is the difference between the teaching ‘style’ in the two resources.

Textbooks tend to follow a model that is very teacher directed while TIPS uses a more student-centred approach. In our experience, teachers and students found it difficult to flip back and forth between lessons within the same unit. After reflecting on the successes and challenges of using TIPS last year, we thought that perhaps beginning with the student-focused type of lessons in a whole unit would make a better transition for students.

If you are trying TIPS4RM for the first time this year, or just using it in a bigger way, please let us know how it is going by clicking on the ‘comment’ button below. We would love to hear successes but of course we will help you with challenges that come up as well. Teachers, if you are experienced with TIPS4RM, please post your advice for those who are beginning this exciting journey in mathematics. You also might want to check out the new Interactive White Board lessons for TIPS4RM that are available at the Ministry’s MathGAINS website.

Welcome back, everyone, and we hope to hear from you on the blog soon.

Pairs Coaching Model

At the recent OAME2011 conference, Andrea and I were asked to provide a brief description of how our Pairs Coaching Model works. We found it quite challenging to explain in the little space provided for the GAINS Coaching Resource Room. We have attached a document that was written in the SDCO (now Learning Forward Ontario) newsletter last spring that more clearly describes how we approach our work as coaches.


If you have any questions or comments about how we work with teachers, please comment here and we would be happy to answer you.

Learning Goals and Success Criteria in Math

As Andrea and I travel to different schools  this year, we have been asked to discuss where Success Criteria fits into a 3-part math lesson. We have been trying out a few different scenarios and want to share our observations so far. We are hoping to hear comments from other math teachers and coaches about what is working well (or not!) with respect to Learning Goals and Success Criteria in your math lessons.

The first time we applied our learning about Learning Goals and Success Criteria, we planned a 3-part problem solving lesson using Bansho. The curriculum expectation we wanted to cover was about students being able to determine when each operation was appropriate to use. This was an easy one to convert to kid-friendly Learning Goal language. The problem we chose could have been solved using a combination of any of the four basic operations (adding, subtracting, multiplying or dividing) but the most efficient way would have involved division. The teacher was hoping to determine how flexible her students were with choosing operations to solve an open problem, especially division. So far so good, right?

Well, we really hit a wall with the idea of co-constructing the success criteria. First, the students had never participated in Bansho before and would not be able to explain how to be successful at something that was brand new. Our second wall was that we did not want to tell the students to use division. We were hoping to see a variety of operations used and to use Bansho to have the students analyze the methods and reflect on ways they might try if given another, similar problem. We wanted a variety of solutions and strategies at this point. So, we created what we called Success Criteria that really just described what they would be doing at each stage of the lesson. What the teacher WAS able to do (after three more problem solving lessons involving Bansho), was to then co-create Success criteria for problem solving in math class. The students were able to reflect on what they did that was successful and create the criteria to refer to in future problem solving situations.

Since then, we have been working in a few more schools that are focusing on planning and communicating clear Learning Goals in Mathematics. Here is a picture of the Learning Goals and co-constructed Success criteria from our most recent school. We will report on our progress in  future posts.

learning goals and s crit

If you have been involved with this type of learning in your school, we would love to hear from you. Have you considered ways to get the learning goal across while maintaining a constructivist approach in Problem Solving? How have using Learning Goals and/or Success criteria helped your students? We look forward to continuing this learning process together.

Wired Math and Bloom’s

Engaging students in difficult mathematics problems is often challenging in the intermediate grades. I’ve had some interesting discussions with teachers lately around two topics that are closely connected to student engagement. The first is using Bloom’s Taxonomy when planning a unit in Math to help students learn in a more constructivist way. The second is using technology as a tool to engage students. After more discussion, we found that these can be used together quite nicely. Looking at the site, Educational Origami, we have been looking at ways the author, Andrew Churches, suggests to use technology in the classroom at each level of Bloom’s. This site includes the instruction sheets for students to use the technology, and it also describes how the activity relates to Bloom’s taxonomy and many contain a 4-level rubric. Check it out, you might get inspired!

Another site that has been sent to me is the Wired Math site. This has games and simulations for each strand of math for grades 7, 8, 9 and 10. Wired Math has games that help students practice skills in a more engaging way. What level of Bloom’s Taxonomy are students working at when they engage with Gizmos? This site is licensed for all grade 7-12 students in Ontario’s publicly funded schools. Highly recommend the visualizations to help students with abstract concepts.

CLIPS Improve Gr. 7-12 Student Learning

January can bring on the doldrums for a lot of us with the grey skies and slushy weather. Our students are probably feeling the same way. Why not try something different to inspire the kids in math? The online resource called CLIPS (Critical Learning Instructional Paths Supports) might be just what your students need to get excited about learning important topics in mathematics. Although there are only a few clusters of expectations represented for each grade right now, they are really showing some good results and are being added to all the time.

Make gains with CLIPS by:
1. Planning Lesson Sequences
2. Teaching in the Digital World
3. Engaging Learners
4. Reaching All Students
5. Building Professional Knowledge

At this link, you can read a brief fact sheet about ways this resource is being used by Ontario teachers. There are always new CLIPS being added so bookmark the site and revisit throughout the year. To access the CLIPS for teachers information click here.

To visit the CLIPS for students page, click here.

At the site, students can click on the Toolbox icon and get linked directly to virtual manipulatives, interactive graphing tools, specialized papers and more. This would be a great site to share with parents as well.

Mental Math at the Border?

Yesterday, after a successful day of cross-border shopping, I was sent in to the Canadian Customs building to pay my taxes. Everyone was being pulled in and it was very busy. As I observed the border agent trying to determine the value of the taxable items on each of my bills I had an ‘aha‘ moment. He was struggling to use Mental Math strategies to add the items together! He lost track while adding the taxable items a couple of times. Then he tried to add all of the non-taxable items and subtract them from the total. Unfortunately, there were more non-taxable items so there were too many numbers to keep track of and this strategy failed. Finally, counting, working from the bottom of the bill and counting-up using the values rounded to the nearest dollar, the amount was determined. The agent was getting frustrated with the task but I’m sure the long lines and noisy people made it more difficult than other times. I wonder who else has to use Mental Math strategies in their daily work?

I tell you this story because Andrea and I, and several grade 7 and 8 teachers, have recently discussed the need for students to have a repertoire of Mental Math skills to help them in their daily life. My experience at the Customs office has inspired me to ask for help with creating some work-stations and open questions designed to give students more exposure to real-life situations where these skills will help them.

This holiday season, if you notice a time that you, or someone in a specific job, needs Mental Math skills, please post the scenario on this blog by clicking on the Comments link above (or send me an email if you are shy).

For example, think about Mental Math needed if you are:

  • shopping
  • planning a party
  • wrapping gifts
  • storing items
  • cooking

We will use your stories and examples to compile the questions and work-station ideas. We can share them with all of you by posting them here.

To get started now, here is a video to teach kids the basics of Mental Math. The Secret to Rapid Mental Math

To get a look at how the basic strategies are taught, visit this list from Saskatchewan. It seems like a good idea to review some of these (especially multiplication) with students in higher grades. Strategies for Mental Math

Thanks for your help with this collaborative project!

Multiplication Game

Thanks to Andrea for finding this great Multiplication game. Students really need to be flexible with factors and multiples in Intermediate mathematics. Students working on fractions should really refresh their skills in Multiplication in order to do well. What better way than with a game! Visit the Math4Love blog and read about the Damult Dice game (so easy!). One of our schools tried it this week and the students were really engaged. I’m going to try it with my son this weekend. Post a comment and tell us how this (or other multiplication game) has worked in your class.