Big Results in a Small Amount of Time

On May 17, 2016 over 150 teachers gathered to explore, discuss and make connections.  After a long day at work, these teachers eagerly investigated and shared ideas regarding how to use ‘5 Mathematical Routines’ (Quick Images, Counting, Number Talks, Number Lines and Which One Doesn’t Belong) in their classrooms.   These 5 – 15 minute routines help to develop a mathematical community, provide regular practice on mathematical concepts, develop number sense and computational fluency with the students.

“The ultimate goal is that students make connections over time, build an understanding of relationships among numbers and operations, and ultimately apply their number sense understanding to problem solving.”                                                                                ~Jessica Shumway

These routines are directly connected to the B.C. revised curriculum.  The focus on curricular competencies to ‘show what you know’ (the content) is embedded in all of these routines. Each routine has a slightly different emphasis and purpose, but all of them focus on communicating, thinking and working together (the Core Competences). The structures of routines may include being part of a ‘warm up’, daily math investigation, mini-lesson, guided math group, or a ‘reflect and share’ session.

Here is a description of the 5 routines focused on during the session:

Quick images

• Students are shown pictures displaying groups of objects or symbols, viewing each for only a few moments.
• Students are encouraged to take a ‘picture’ and visualize the image in their head.
• Students are asked to share their thinking about the images shown (i.e. How do you see it?)

Counting

• Counting Around the Circle – Whole class participation. Each student says a number as you count around the circle.
• Counting Collections – Partner work. Each pair is given a collection of objects to estimate, count and record the count.
• Choral Counting – Whole class participation (or small group). The teacher decides on a number to start on and then a number to skip count by.  The teacher records the number, pausing the count at a strategic moment and ask questions. The goal is not just practice rote counting, but to engage the children in reasoning, predicting and justifying.

Number Talks

Conversations with the whole class that are usually about 5 – 10 minutes in length.

• Intended to help develop conceptual understanding and efficiency with number.
• The teacher presents a mental math problem.
• Students are asked to think about the problem and then share solutions and explain thinking.
• The teacher acts as a facilitator to guide the conversation.

Number Lines

• Numbers are represented as points and distance on a line.
• They provide representation of the relationships of number and the spatial sense of quantities and magnitude.
• Teachers use number lines to represent numbers and support reasoning about them.
• Open number lines provide flexibility in thinking. Students are asked where they might place a number in relationship to another number.
• Open number lines are also used to help students add and subtract numbers and demonstrate their reasoning.

Which One Doesn’t Belong – wodb.ca (see examples on this website)

• Students are presented with four different numbers, objects or shapes (that are alike and different in many ways)
• Questions are asked:
  • What do you notice?
  • What makes all the items alike?
  • What makes them different?
  • Which one doesn’t belong?
• Students explain and justify their choice

Each of these routines only take a small amount of time but when used consistently…they will help to build your students’ understanding, confidence and ability to communicate their thinking. Are your students able to make connections, communicate their thinking and see themselves as competent and confidence mathematicians?

Please see the PowerPoint presentation and resources connected to this post on the Big Results in a Small Amount of Time page for more examples and clarification.

Take the time out of your day to use one of these 5 routines and let me know how it goes!

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What Really Counts?

In April I was extremely lucky to attend the NCTM conference in Boston Massachusetts. I listened to a fabulous session titled ‘Counting Matters: Why We Should Pay More Attention to Counting’. The presenters (Elham Kazemi, Allison Hintz, Kassia Omohundro Wedekind, Teresa Lind, and Angela Chan Turrou) were so enthusiastic and engaging. I knew I had to return to my district and try some of the routines presented from Jessica Shumway’s book ‘Number Sense Routines’.

With great excitement I collected materials and ventured out to several schools to try out my new discoveries. Thanks to all my wonderful colleagues (Sarah Schnare, Carrie Donahue, Cara Johns, and Amanda Crawford) for sharing their students with us. My wonderful friend and ‘partner in crime’, Lillah Martin, joined me on the journey. We learned so much from the students that we needed to share the experience with others.

On May 12 an amazing group of around 80 teachers met and uncovered the power of two ‘counting routines’ in the Primary classrooms (counting collections and choral counting). I am always astonished by the devotion of teachers who attend after school workshops. The group explored counting collections, and choral counting while making connections to important math concepts and seeking out patterns.

Learning to count while simultaneously developing a sense of quantities and number relationships is an important foundation for students. Counting is more than repeating a rote sequence and recognizing the numerals. Counting has proven to be important to lay the foundation for understanding of the base-ten system, operating on numbers and problem solving. When students develop competence, they not only count with accuracy and ease, but will also develop the sense of the quantity of numbers they are working with. The focus moves from knowing the number they landed on to making reasonable estimated and noting the reasonableness of the outcome of the counting.

I challenge you to try out these routines with your students to uncover the important math concepts and rediscover the joy of counting.

Please check out this link http://tedd.org/ for additional information. Again, thanks for the amazing presenters and Twitter friends of the NCTM Boston session.

Counting on Fall – Math in Nature

There is a new series of books called “Math in Nature” which journeys into the natural world.  The wonders of nature are shown in vibrant cut paper collages that focus on important mathematical concepts. Each season focuses on an area of mathematics. There are many  ‘What if?’ problems presented in the text.

On the day before Halloween (can you believe it!), 60 primary teachers gathered at DEC to discover and experience activities that promote number sense with Chris Hunter and myself.  We emphasized the importance of differentiating the activities to meet the need of the students.  Assessment for learning is another important aspect to consider when doing these activities with students.  Ask yourself: What do I want the students to know, understand or be able to do?

Here are some of the activities that extended from the ideas in the book:

1. Guess, Check and Estimate – (focus on estimation, referents and skip counting)

• Ask the students take a collection of objects and lay them on the bare tree
• Ask the students to ‘estimate’ how many objects are on the tree board
• Ask the students to make a ‘referent’ of 2, 5, or 10 and pull it away from the total collection
• Ask the students if they would like to revise their estimation (after seeing the referent)

2.  Bat Cave Pattern – (focus on patterning)

What patterns do you see?

• How could you model the patterns using Cuisenaire rods? (or other materials)
• Some students may need to lay rods directly on the book.
• Some student may need to be challenged by changing the number of bats sleeping in each row (increasing by 2)

3.  Making Ten Story Mats – (focus on partitioning and number operations)Ask the students to count out a quantity of 10 objects.

• How many different ways can you make 10 in two parts?
• What stories can you tell about your story mat? (I counted 5 leaves on the ground and 5 floating in the sky.  How many leaves have fallen from the tree?)
• What equations can you write about your story?

4. Roll, Build and Compare – (focus on comparing quantities…more/less/the same)

• Ask the students to work with a partner.
• Each partner rolls a 10-sided die and builds the quantity rolled on their 10 frame.
• The partners compare their quantities.  Who has more? less? Are they the same?
• Ask the partners to determine how many more or less.

Daily Math Investigations

The daily calendar has been a routine in many primary classrooms since the 1970’s when Math Their Way created it. It was revolutionary in those days. It was viewed as an opportunity to expose students to patterns and counting.  Calendar was considered an important part of daily math instruction.

In its original form, it was a fairly passive experience for children. Most young learners watched as one of their peers completed a pattern, listened as others counted, or chanted along with the group. While we recognize the value of daily exposure to mathematical ideas, the passive nature of this imagining of calendar often did not meet the needs of many of our learners.

What we have learned and are continuing to learn about the brain, how children acquire mathematical concepts, and developmentally appropriate practice has lead us to re-examine this traditional approach.

Carole Fullerton and I decided we needed to “Kill the calendar”!  In many of the classrooms we were working in, students (not to mention the teachers) often seemed disengaged with the calendar routines. We decided to create the resource called ‘Daily Math Investigations’. In this resource, we present a more active, participatory version of “calendar” – a daily opportunity for students to truly engage with meaningful math concepts, to play with materials, to process, think, and problem-solve. The tasks, questions and problems we have included in this resource are intended to inspire thoughtful math investigations into number, shape, measurement and pattern. Daily Math Investigations allow students to explore math concepts in real and embedded ways.

Daily Math Investigations are an opportunity for students to think and play with mathematical ideas. Teachers present tasks and pose questions that are intended to promote curiosity about numeracy concepts. In opening up the kinds of questions we ask, we include more students in the learning of math, and help to address the range of learners in our classrooms. A combination of entry tasks and rich routines allow for balance between whole group, small group and independent learning, a chance for students to explore the math at their level.

A monthly calendar gives us interesting information. We can use it to mark important events, like an upcoming holiday, a student’s birthday or a school celebration. Highlighting these events on a calendar and counting the days until they happen is fun for students.

For many of us, calendar time (and all of the activities associated with it) is ingrained in our script for primary teaching. It’s important, however, to consider carefully the purpose of these tasks – and more importantly, their effectiveness. We don’t believe in ‘throwing the baby out with the bath water’. But ask yourself, “What should I keep?”  “What should I let go?”

Ask yourself a few questions:

1. Are the pieces of my calendar routine truly relevant?
2. Are students talking about the math?
3. Are the students engaged?
4. Are the students doing math?

Thank you, Carole, for sharing your wonderful ideas.  If you’d like to get a copy of “Daily Math Investigations’, please go to Carole Fullerton’s blog, http://mindfull.wordpress.com/.

On October 22, 2013 over 80 amazing teachers attended an afterschool in-service about ‘Daily Math Investigations.’  As they entered the room, they were invited to ‘engage in’ and explore several ‘Entry Tasks’.  The room was full of conversations, discovery and engagement.  They were talking and doing the math.  This is the vision for all primary classrooms.  What do you think?

Halloween Fun

With Halloween just around the corner , I stopped by the neighborhood ‘Dollarama’ to get inspiration for some Literacy and Numeracy centres.  It was amazing what I discovered.  Here are some of the materials and ideas that were generated by the Early Literacy and Numeracy teachers that I am so lucky to work with.

The Power of Two – Linking Literature with Mathematics

My passion for wonderful picture books and excitement of teaching math in engaging, relevant ways has helped me link the power of literature with mathematics. Both Literacy and Numeracy involve the interconnection of skills and concepts, have developmental patterns of learning and focus on thinking and making sense. We want our students to comprehend when they read and to understand the math they are doing. Engaging picture books can be effective vehicles for motivating children to think and reason mathematically. Often the books can provide a starting point to introduce a new mathematical concept. By reading and acting out a story, all our learners have the opportunity to absorb the information – our auditory learners hear the story, our visual learners see the story and our kinesthetic learners can feel the story. It is all about the learners. It is still important that we provide the concrete tools for our students to explore and make their own connections using manipulatives. Good books do not replace hands-on experiences. Choose one of the books and tasks included in this presentation and discover ways that will allow all your students to build mathematical understanding and make connections to math in their world. Enjoy!

Building the Bridge – Linking Reading and Writing

The Golden Oldies are still important. Resurrecting the tools from long ago happened at our last session on April 8, 2013. The session ‘Building a Bridge ~Linking Reading and Writing’ was well attended by passionate Primary educators.  Lillah and I began our teaching using the ‘Ann Ingham’ tool sounds and their stories.  We noticed that somewhere along the journey, these valuable tools have disappeared or are often hidden in classrooms.  One teacher commented on how she felt relieved that she “doesn’t have to feel bad about using the tools with the stories” with her students.  Somehow she felt that these ‘tools and their stories’ were not seen as ‘best teaching practices’. We revived and recreated the tools to be more appealing and updated for today’s classrooms.

Students need to make connections and learn to apply ‘phonetic tools’ to their reading and writing.  Explicitly teaching these tools and allowing the students to explore, discover and make inquiries with them is required.  Our role as a teacher is to fill the students’ lives with engaging, interactive and developmentally appropriate experiences that are both playful and purposeful.  Asking students to fill in worksheets does not meet the criteria.  Searching for words, applying the tools, and authentic practice ways allows students to make connections.

Research supports that reading and writing are different processes that share a reciprocal relationship.  Understanding this will allow us to scaffold and differentiate our instruction for our learners.  By providing them with the right ‘tools’ they will ensure what they read and write makes sense, sounds read and looks right.