Provocation can be defined as the act of causing someone to feel, think or begin to do something. In the Reggio Emilia approach to learning they involve the teacher creating invitations/ displays that provoke students to begin to explore an idea or concept with materials that spark thinking. Provocation materials can be loose parts, natural items, children’s literature, photographs, inquiry questions or all of the above. The goal is to find something that sparks curiosity and leads to new learning.
Within mathematics, provocations can lead to inquiry and discovery of mathematical concepts and initiate mathematical thinking. I am currently working with a group of four exceptional kindergarten teachers to develop opportunities for our elementary teachers to explore the idea of using provocations as a tool to provoke mathematical inquiry, creativity, and discussions. Together we initiated the first ever Kindergarten Mathematics Learning Community in which kindergarten teachers come together to discuss ways to provoke their young mathematicians in thinking and growing mathematically.
Our first provocation focused on the question How do Numbers Help Me Tell My Story? This question and the materials we deliberately put together can serve as a starting point for developing a deeper understanding of numbers and counting concepts in Kindergarten.
Some of the Big Ideas of Counting that can be explored through this provocation are:
- You say one and only one number for each object (one to one correspondence)
- The last number spoken tells how many. (cardinal principle)
- You can represent a number in a variety of ways.
- The quantity of a group does not change if the objects are rearranged. (stability)
- There is a consistent set of counting words that never changes. (stable order principle)
- You say one number name for each object tagged. (synchrony)
Our How do numbers help me tell my story? provocation included a variety of loose parts (shells, buttons, rocks, glass beards, pipe cleaners etc.) as well as tree cookies with numbers printed on them and wooden numbers. We used felt squares to delineate the space and added round cork pot holders. Looking in the mirror students could study themselves to recreate what they see using the loose parts. They can also think about numbers that connect to themselves and represent those numbers using the loose parts on the counting place mats as a guide.
Using high quality children’s literature to connect mathematical concepts, and cultural perspectives is an important consideration for us in every provocation we design. The Colors of Us was our inspiration for our How do numbers help me tell my story? provocation. Other literature connections can include The Best Part of Me, and Every Buddy Counts.
For those of you wanting to provoke the thinking of our young mathematicians I am including a freebie to get you started. Here are the counting mats I created in French and in English as well as the Number Formation Cards. Enjoy!!
This exploration of Provocations in mathematics is has become a wonderful learning journey for me. I am so honored to have an opportunity to learn with some fantastic teachers within my school division and around the world. If you are looking for inspirations from leaders in this area make sure to check out the work of Janice Novakowski.
At the beginning of the school year I was fortunate enough to work with many dedicated teachers around the idea of Mathematician’s Workshop. Our day together revolved around a framework I had created as a consolidation of my learning about successful mathematics instruction in the classroom. This is a synthesis of many ideas from many mathematics educators and experts.
To explain my thinking of this model and to provide an example of how it is working in a classroom I was fortunate enough to have an opportunity to create a Periscope with one of my session participants. Mrs. Colleen Johnson was so very generous with her time and expertise to share how she is making Mathematician’s Workshop live in here grade 4/5 classroom.
I have spent the last 3 days listening to, learning from, and devouring the words of great teachers. Debbie Miller, Patrick Allan, and Penny Kittle have reminded me of the bliss that comes from teaching students how to read and write using authentic experiences with reading and writing. Authentic moments where you connect the students to their inner reader by helping them find the texts that matter to them and engage them in ways that only powerful text can. Authentic moments that connect them to their inner writer by standing on the shoulders of “beautiful words” from others like Sarah Kay, and writing about things that evoke their passions. If I could take away one word…one message…one thought from these last three days it would be Authentic!!!
For these great teachers- Debbie, Patrick, and Penny authentic is about providing students with opportunities to engage in reading and writing in ways that are meaningful, interesting, and relevant to students as individuals. In their classrooms they provide students with time to connect with great books while they take the time to confer with students. In writing they provide students with time to write as they themselves share their own writing both finished products and works in progress. This kind of teaching is not born from worksheets, packaged programs, and activities that do nothing more that fill the time. It comes from relationships, sitting side by side with students, and taking to them about their lives as readers and writers.
These 3 days have provided me with time to think about what this could look like in mathematics. Can we take these ideas and put them into our mathematics classrooms? Can we help students connect as mathematicians who learn from the “beautiful” math of others? Can we model our own mathematics work and how we engage in mathematics? Can we provide students with time to actively engage in rich authentic mathematics that provokes thinking, and passion?
This type of mathematics is about more than completing the worksheet, or the page in the textbook. It is about fostering the conditions for student to become mathematicians who don’t just do math but think mathematically. My mind is swimming with the possibilities of re-imagining what the Mathematics Workshop could look like so that it would foster mathematicians. I think it is possible.
One thing is clear though. The most important thing that we as teachers need is an unwavering belief that all kids are capable of becoming mathematicians and deserve the time to dig into authentic mathematical experiences.
I love to play cards. It is a love that has been instilled in me by my parents and grandparents. Now I am lucky enough to have my kids picking up this love from my family. The joy for me comes not only from the game but from the memories of get seeing 4 generations of my family sitting around a table sharing time together, conversations, and fun. My kids have 3 favorite games that they have been taught by their great grandparents. They ask to play them every time we are all together. These games are great for the kids because they are easy to learn and also allow them to use their ever growing skills in mathematics. I wanted to share them with you. Maybe they will become an opportunity for you to sit around a table with your own children and #PlayMath.
Chase the Ace
The object of the game is to not not be stuck with the lowest card. In this game the kings are high and aces are low. To play this game you need a standard set of cards and three counters per person (nickles, paperclips, buttons…). The dealer deals out one card to each player. Each player then looks at their card and determines whether or not they want to keep it or trade it with the person to their left. The player to the left of the dealer starts by saying “keep” if they want to keep the card or trades it with the person to their left by sliding it face down to the player. That player must then exchange cards with the player wanting to change unless they have a king. If they have a king they lay the king down face up and show the rest of the players as proof. Having the king makes them immune to trades for that round. If that happens the trade can not occur and the player must keep the card. The big risk comes in when changing your card because you always run the risk of changing for a lower card. After the exchange has taken place the player who was forced to trade looks a their card. They then decide if they want to stand or change with the player to their left. Play continues around the table until it reaches the dealer. If the dealer wants to exchange cards they turn theirs up and cut the deck. The card they cut becomes their card.
Once the play is back to the dealer all players lay their card down face up for all to see. The player with the lowest card places one of their counters into the pot. If more than one player has the lowest card, each player with the low card must place a counter into the pot. The cards are collected to be shuffled and dealt by the next player to the left of the dealer. In this way the role of the dealer also goes around the table.
Once a player loses all their counters they are out of the game. The winner is the last player to still have a counter.
Sticks- A Game of Sets and Runs
This is the current favorite around the table. All you need to play is a set of large Popsicle sticks (we bought ours from the dollar store) and a deck of cards. My mom actually made 2 sets. One that is more challenging for us adults, and a junior version for the kids. In this way everyone is playing together. The object of this game is to successfully accomplish the task on your stick before someone around the table goes out. To go out you are able to get rid of all of your cards by laying out your own sets and runs or by playing on the sets and runs of others. Each time you accomplish a task you “earn” your stick and can turn it face up. The first person to earn seven sticks wins.
Full Rules can be found at E How Sticks Card Game
Our list of Adult and Junior Sticks- Sticks
What can I say…we love this game. It’s fun, it’s easy, and their is nothing better that sticking a “Pick Up 4” to a loved one.
For more games and resources check out the links below:
- Games to Play with a Deck of Cards – This booklet is created by Math Coach’s Corner. It is a great collection of games that can be copied into a small booklet. I think this would make a great gift for families at a Math Night or other such events.
- Acing Math– This 69 page booklet features games, for grades K though 6 children, that can be played with a standard deck of cards. It’s an amazing resource.
Have Fun and PlayMath!!
I am always on the look out for ways I can support my children in extending their learning of mathematics at home. Sometimes these opportunities take the form of problems we solve or apps that I share with them and sometimes they take the form of games we play. Our Saskatchewan Curriculum has 4 distinct and interconnected goals for Mathematics Education. These goals are:
- Logical Thinking
- Number Sense
- Spatial Sense
- Mathematics as a Human Endeavour
When I look for games we can play I always think about which of these goals they support and most importantly is this fun. Here are some of our current favorites for Playing Math!
Logic Links– a series of puzzles that make you think. Each puzzle is comprised of a series of clues that are solved by arranging the coloured chips in a certain order. This is a great game to develop Logical Thinking.
Noodlers– this is a fantastic game for teaching spatial sense and problem solving. To play you use the recommended number of sticks to divide up the surface of the card to separate the shapes on it. This is a great game to develop Spatial Sense.
Q-bitz Extreme– in this game players each get their own Q-bitz Extreme board with 16 cubes, and race to be the first to replicate the curving patter to win the card. This is a great game to develop Spatial Sense.
There is so much math in cooking…math that is just waiting for you to point out to your children as you engage in the process of making something together. From a very young age my children have been by my side while I cook. As they get older they have been taking on a greater role in the process. They dump in ingredients, measure, stir, and of course lick the spoon. I have found that these moments provide us not only with a chance to be together, but also an opportunity to Talk Math. Cooking involves math. Creating lists for and counting out ingredients, estimating how much we may need, fractions with measuring cups, counting cups, figuring out how long to bake the food for, and creating serving sizes all involve math and mathematical thinking.
Do we have what we need?
Is that enough?
Which one is 1/2 cup ? How many to make 1 cup?
How long should we cook it for?
Does it taste okay? What more could we add?
Do you know that cooking involves math? Where do you see math in this recipe?
By asking these questions and many others you are bringing math to your child’s attention and creating a conversation about how we use math in our lives. In this way you also show your child that math is something that we can do together, and have fun with.
So grab your kids and your recipe book and find a way to enjoy some time together while you cook and Talk Math.
My career has taken me from Classroom Teacher to Instructional Consultant to Vice Principal to my current position as the Acting Coordinator of Mathematics. Throughout this journey I have had many opportunities to talk with parents about learning. By far the most common question that I get asked during these conversations is “How can I help my child succeed in mathematics?”. There are so many possible answers to this one question. So much so that I can not cover them all in one blog post. So given the plethora of possibilities I have decided to create a series of posts that highlight some of the things that I have done or currently do with my own kids age 7, 11 and 14. I am going to share with you my efforts, as a parent, to create the conditions for my children to succeed in mathematics. These possibilities are not intended to be a checklist of everything you should do but rather suggestions of what you could do.
I am going to start with what I believe the most important thing you can do… Value Math. As with most things your child takes their cues from you. Their beliefs, values, attitudes are often your beliefs, values and attitudes. If you think something is important so will they. As a teacher, I would inwardly groan every time I heard a parent say “It’s okay that my child is not good at math…I wasn’t”. This message instantly devalues mathematics and lets your child know that they can devalue it too. By devaluing mathematics it creates a constant struggle between the teacher and your child every time they engage in learning mathematics. My number one recommendation would be to not create this battle. Instead, let your child know that you value math.
With my kids I constantly reinforce 5 key messages about valuing mathematics.
- Math is Important– I think math is important in the world and I let my kids know it every chance I get. When I see math, I point it out. I talk to my kids about future career opportunities for them and what math they require to make that happen. I share with them how I use math to manage our household, where I use it in my career, and where it exists in the careers of others. My children know that math opens opportunities for them, and that they need it to be an engaged and informed citizens.
- Math is Fun– Math can be fun. I am constantly looking for ways to “play” with mathematics. I want my children to want to engage in mathematics and like everything, if it is fun they want to do it. I look for mathematics games, puzzles, and challenges they can do by themselves, or that we can do together. Our closet is full of games that build mathematical understanding and are fun.
- Math is Hard (sometimes)– My kids need to understand that sometimes math is challenging and in these cases persistence is necessary. I expect my children to face these challenges with a positive attitude and determination. I am always there to help them when needed but my job is not to rescue them. When my kids hit a question that is challenging I let them struggle. Yep I said it…I LET THEM STRUGGLE. Instead of sweeping in with the answer I choose to stand back and just offer encouragement. You can do this!! I believe in you!! Do the best you can!! I am so proud of you for not quitting! Look back to see if you can find a similar problem. How do you think you should do it? This standing back is sometimes hard to do but trust me… the empowerment they feel when they figure it out on their own is so worth it. They learn the math, but more importantly they learn that they are capable of meeting challenges and that persistence is necessary. This does not mean that I never help them. Sometimes, after what I feel is an appropriate amount of struggle I do step in. My goal is not to never help them. Instead, my goal is to build their persistence and their confidence in themselves first.
- Math is Problem Solving– Math is more than just computation. Math is about encountering a problem and then using mathematical thinking to figure it out. I often place problems in front of my kids and ask them for their advice. These aren’t problems that are written on paper about two trains leaving a station… or other things you may see in textbooks. Instead these are problems that I encounter in life. For example, the other day I needed to drive my 7-year-old daughter to her hockey practice, and I had to figure out when to leave the house. The easy thing would have been to just figure it out on my own but instead I saw this as an opportunity to problem solve with my kids. I called my 7-year-old and 11-year-old over and asked them what time we should leave. Because this wasn’t our first ever attempt at problem solving they very quickly identified 3 pieces of information they needed… how long would it take to drive to the rink, how early do we wanted to be there, and what time the practice began. Once they had the information they worked together to find a solution. The best part was that we could actually use their solution and get authentic feedback on if their solution worked. We arrived on time, but more importantly my kids learned that math was alive and relevant!!
- Math is Reasoning– Math is about thinking logically and making sense of situations. By looking for opportunities to allow my kids to engage in mathematical experiences in and out of our home I am trying to enhance their ability to reason. My kids know that math is more than finding a number to an equation…it is about thinking. When I look for mathematical opportunities I am really looking for opportunities for them to think…with me, with others and most importantly for themselves. My every day example has been with providing them with the choice of deciding what to wear for the day. My kids have learned to choose their clothing based on the weather conditions of the day. I share with them the forecast each day, along with the current conditions. Then I ask the question “What would be the best choice in clothing for today?” When they were little I would often use words like cold, hot or warm to describe the temperature. I also talked about the appropriate clothing for cold, hot, and warm weather. Now all I do is give them the forecast and let them make their choices. With my seven-year old I still sometimes veto the choices but for the most part she is expertly reasoning her way through the possibilities with the information she has been given.
Valuing math is so very important to helping your child succeed. I really do believe it is the most important of three suggestions I can give parents. My other two suggestions would be to Talk Math and to Play Math with your child. Over the coming weeks I will continue to expand on these three ideas and share suggestions on this blog and on Twitter. So be on the look out for ideas to #TalkMath, #PlayMath, and #ValueMath.