Authentic Learning- Connecting Literacy to Mathematics

Authentic Learning

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.

If You Give a Kid Some Cards They Will…#PlayMath

Kids with CardsI 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 Cards at the Lakeplay 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

Uno

unoWhat 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!!

Jenn

Building on Mathematical Thinking Through Play! #PlayMath

Games

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:

  1. Logical Thinking
  2. Number Sense
  3. Spatial Sense
  4. 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 LinksLogic 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.

 

 

noodlerNoodlersNoodler2– 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

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.

 

 

Cooking With Your Kids…the Perfect Time to #TalkMath

Cake Sushi Tasty Pi

 

 

 

 

 

 

 

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.

How can you Support your Child with Mathematics? First Off #ValueMath

Kids

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.

  1. 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.
  2. 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.
  3. 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.
  4. 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!!
  5. 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.

Responding to Common Questions Faced as a Math Coordinator

My current role as an Acting Math Coordinator provides me with opportunities to talk with many people about one of my passions…teaching and learning mathematics.  Through conversations I learn from and with others, I clarify my thinking, and I uncover ways that I can offer my support.  Over the past few months in this role I have found myself asked the same questions repeatedly by parents, by teachers, and by administrators.  Each conversation is another opportunity to learn, so I thought I would bring the conversation here…to my blog, a place where we can take the conversation beyond the walls of the schools, and beyond the one on one setting.  It is my hope that by doing this I can invite more ideas and perspectives in and learn with and from you all.  So here goes…I am going to share with you my most common questions and the responses I most often give.  I do this not to share the “right” answer but to invite your thinking and perspective into the response.

Parents Ask…

Why does the “new math” not require kids to know the basic facts?

Response:

Our current Saskatchewan Mathematics Curriculum does require that students learn the basic facts.  In grade 1,  grade 2 and grade 3 curriculum outcomes exist specifically for addition and subtraction.  In grades 3, 4 and 5 outcomes for multiplication and division are listed.  In almost all of these outcomes the process of Mental Math and Estimation is explicitly highlighted as an integral part of the understanding.

According to our curriculum  “Mental mathematics is a combination of cognitive strategies that enhance flexible thinking and number sense. It is calculating mentally and reasoning about the relative size of quantities without the use of external memory aids. Mental mathematics enables students to determine answers and propose strategies without paper and pencil. It improves computational fluency and problem solving by developing efficiency, accuracy, and flexibility.”

Demonstrating understanding of addition, subtraction, multiplication, and division through mental mathematics requires that students learn the basic facts to the degree that they can calculate mentally efficiently, accurately and flexibly.

Teachers ask…

Why are students not retaining the basic facts?

Response:

To this I often respond…it depends.  It depends on the student, their specific learning needs, their learning styles and their previous experiences.  The answers to this question can be as varied as the number of students we teach every day.

However, I do have two working hypotheses as to why some students are having a harder time retaining the facts. My first hypothesis is that they need to continue to develop and strengthen their Number Sense.  Number Sense is the foundation for mental mathematics and enhances a student’s ability to flexibly compute.   As students learn their basic facts they move along a continuum from counting to reasoning to mastery.  The intermediate stage of reasoning or “using what you know to figure out what you don’t know” is fueled by Number Sense.  Without a developed sense of number is can be very difficult for students to reason strategically through the operations.

Computation Learning Continuum

My second hypothesis is that students have not had enough time to practice.  Every student is different, and as such every student requires different amounts of practice to move along the continuum.  As teachers, we need to ensure we provide opportunities for students to practice their basic facts in ways that are targeted to their current needs, engaging, and regular. For many students it is not simply enough to practice these skills only during the month or two where they are working through the Operations Unit.  Often they need regular, targeted, repeated, and short practice times that span the entire school year and beyond.

Teachers Ask…

Should we help students become automatic with their math facts first then focus on Number Sense?

Response:

We should focus on them both at the same time.  Strong Number Sense supports reasoning and reasoning leads to mastery.  Without Number Sense we run the risk of having students memorize sequences of numbers that have no real meaning to them.  Without meaning these sequences of numbers can not be effectively called upon to solve problems, communicate understandings, make connections, and logically reason through mathematical situations.

At the same time, if we do not allow students to practice their basic facts we run the risk of them not having the time they need to master them.  This mastery allows basic computation to move into long term memory which in turn frees up working memory for increasingly sophisticated mathematics.

Teachers Ask…

How do we support English Language Learners in our classrooms?

Response:  

Once again to this question I often say… it depends. Again, each and every student is unique and bring with them specific learning needs, learning styles, and previous experiences.  As teachers we need to get to know our students and their learning needs to really understand how best to support them.

That being said, I often find that students who are just learning English require support in learning and understanding the English language being used in the mathematics classroom. Supports for language development can include:math wall words

  • providing time for students to engage in conversations as part of a supportive community of young mathematicians.
  • using a Math Wall in the classroom that allows students to link the English words used to a symbol or picture of what it is.
  • creating Anchor Charts with students that allow them to connect the words to symbols
  • reading mathematics picture books that allow students to
    hear mathematics being spoken and connected to visuals.

Parents Ask…

How can I help my child with math at home?

Response:

This question is complex as so much of it depends on the child and what their interests and needs are.  There simply is no one size fits all response.  However, I do have some ideas…each of which I think requires a blog post of their own to adequately describe and share.  Some quick responses might be:

  • Play– find games that you can play with your child that invite them to use math.  Common games can involve cards and dice that require computation…but be on the look out for opportunities to use math in other ways too.  Games that require logical reasoning and problem solving are also mathematics and can help your child see math as more than just computation.
  • Talk– find ways to talk about mathematics as it exists in your world.  Look for examples of math in grocery stores, as you are driving in the car, on television, and in your kitchen.  If you find yourself using or seeing math share that with your child and start a conversation.  These conversations can help them see that math is alive in our world and is useful.
  • Value– if you value mathematics so will your child.  Share with your child that math is a valuable and important subject for them to learn AND that you will support them along their learning journey.

So there you have it.  Some common questions and my common responses.  Now I would like to invite you into the conversation.  What do you think?  What are your common questions?  What would you add to, or change in  my responses?

I look forward to learning with you as we all work to support teaching and learning in mathematics.

Responding to Common Questions– Powerpoint

It’s Been Awhile…Lessons Learned as a New Administrator

 

It has been awhile since I have blogged.  A long while.  So much has changed for me since I last blogged.  I could give the excuse that I have been busy with my family…which I have, but that is not it.  I could say it has been awhile because I switched careers and moved from consultant to vice principal at an inner city school, but that is not it.  I could say it is because I am back teaching grade two after four years out of the classroom, but that is not it.  I could say it is because I was finishing my master’s degree…which I did (yay!), but that is not it either.  I have not blogged because I could not get my thoughts together in a way that is coherent, organized and what I thought would be “blog worthy”.  So much has changed for me.  So much has been new and I honestly have been treading water, barely keeping my head afloat with so much change.  The learning curve has been straight up.

What’s different now, after 6 months in a school that brought me back to my blog?  I’m not sure to be honest but I can say that for the first time this weekend I had a moment to think, to feel centered, feel at peace with where I am, and in that moment it occurred to me that I am no longer treading…I am swimming! So in this moment of swimming I reflect on what I have learned during these last few months as I have transitioned from a consultant to a vice principal.

  1. There is absolutely a theory/ practice gap and this is NOT because teachers don’t want to implement the theory.  For me the gap exists in my practice when the needs of my students trump the theory I am trying to implement.  Every day I work and learn with children ages 4-13.  They are amazing individuals who are just that…individuals.  Each and every one of them comes to school each day with needs that they look to us to help them with and sometimes these needs are not the same as the lesson I have planned.  This does not mean that I don’t teach, in fact I do everyday.  What it does mean is that I sometimes have to change my plans to meet the needs of my students, and I don’t apologize for this.
  2. Learning in my classroom takes longer than I think it should and that is okay…in fact that should be celebrated!!   I spent 6 months coming to this important realization.  I felt defeated every time the lesson I planned took a week instead of a period.  My timing was off and I was down on myself for it. Prior to becoming a consultant I had great timing.  I could plan a lesson for a period and it would be completed within that period.  What was I doing wrong?  My ah ha moment came when I realized that I am a different teacher than I used to be.  I assess more in the moment than ever before and in those moments I make changes, shift ideas, and adapt to meet the needs of the students in front of me.  I embrace every teachable moment as it comes my way which means that I don’t always complete my lesson but I DO support my students reach the learning goals.  I am no longer driven by the lesson plan.  I am now driven by the needs of the students.  Instead of beating myself up for not achieving the plan I need to celebrate helping my students meet the goal.
  3.  Being a VP means I now have 153 kids.  I have always thought of the students in my class as my kids.  I spend my day with them, come to know them, and love them.  I laugh with them, cry with them, and learn with them.   My students consume my thoughts, keep me up at night, and always make me so proud.  What I have come to realize of myself as a VP is that each kid in the school is now mine too.  I now have a class of 153 students which at times is very overwhelming.  There are so many needs to meet and like a class some of my kids take more of my time and energy but each of them is mine to care for, love, and teach.
  4. I can’t implement everything at once and I am going to have to be okay with that.  I had 4 years to learn so much when I was a consultant.  4 years of stock piling ideas, taking pictures and dreaming about being back in a school.  At first I thought I could jump in and implement everything I had waited so long to try.  I wanted to do it all at once and was upset with myself when I couldn’t find the time to make it all happen.  I’m over this!  One idea at a time, one day at a time.  That is my new motto.
  5. I don’t always know what to do (and am now not afraid to admit it).  As a new school based leader I believed it was important for me to know what to do.  I felt I should have the answers to the questions, the solutions to the problems, the next steps at my fingertips.  I felt that the teachers, students, and parents were looking to me for this, and I felt the pressure of this self-imposed expectation.  I now know that I don’t have all of the answers and can freely admit this to others.  What I can also do is give myself the freedom that comes from not reacting with instant “solutions” but from taking some time to think, ask questions, and invite other perspectives.  In the end my actions are more informed and successful.
  6. I am so very happy to be back in a school as a teacher and as an administrator.  It is by far the toughest job I have ever had but it is also the most rewarding.   I see every day the impact I am having.  Daily, I am energized by the laughter, smiles, and learning of children.   I am blessed to spend my days with some truly amazing people.