Math, Saskatchewan Curricula, Teaching and Instruction

Responding to Common Questions Faced as a Math Coordinator

https://www.flickr.com/photos/desiitaly/2201907500/
https://www.flickr.com/photos/desiitaly/2201907500/

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

Learning, Math, Saskatchewan Curricula

Subitizing- A Fundamental Skill for Primary Mathematicians

Subitizing is the ability to instantly see how many in a small collection of items without counting.  Dots on a die, shapes on a playing card, number of fingers held up on a hand, are all examples of subitizing in action.  In order to subitize successfully students need to see the whole as a collection of objects as well as the individual units.  Subitizing is considered to be a fundamental skill for supporting students understanding of number and ability to perform number operations.

In the primary years students should be given regular and consistent opportunities to subitize in order to build their skills, improve number sense and lay the foundation for future mathematical learning.  In kindergarten numbers to 5 should be focused on for instant recognition.  Once students are familiar with familiar representations of 1 to 5, larger collections can be used to encourage students part-part-whole thinking.   For example, on the card below students may instantly recognize a three and a four and then add the numbers together to know that there is a collection of seven dots on the card.

dot card

As the collections get larger students can be encouraged to use their estimation skills to think about “how many” and “how do you know”.  Our Saskatchewan Curriculum refers to this fundamental skill through several outcomes from Kindergarten to Grade 2:

  • Kindergarten- NK.2 Recognize, at a glance, and name familiar arrangements of 1 to 5 objects, dots, or pictures.
  • Grade 1- N1.2 Recognize, at a glance, and name familiar arrangements of 1 to 10 objects, dots, and pictures
  • Grade 2- N2.1 Demonstrate understanding of whole numbers to 100 (concretely, pictorially, physically, orally, in writing, and symbolically) by: 
    • representing (including place value)
    • describing skip counting
    • differentiating between odd and even numbers
    • estimating with referents
    • comparing two numbers
    • ordering three or more numbers.

This video is an excellent example of a kindergarten teacher who is using Quick Images to build on her students subitization skills, and create opportunities for mathematical conversation.

subitizing video

Information about Subitizing

Subitizing-What is it? Why Teach it?

Pinterest Board on Subitizing

Resources to support teaching Subitizing

Dot Cards and Ten Frames

Sparklebox Dot Cards