Big Results in a Small Amount of Time

On May 17, 2016 over 150 teachers gathered to explore, discuss and make Big results 1connections.  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 Number Sense Routinesunderstanding 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:Big results 3

Quick images

  • Big results 4Students are shown pictures displaying groups of objects or symbols, viewing each for only a few moments.
  • Students are encouraged to take a ‘picture’ Big results 5and 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.Big results 6
  • 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 Big results 7moment and ask questions. The goal is not just practice rote counting, but to engage the children in reasoning, predicting and justifying.

Number Talks

Big results 9Conversations with the whole class that are usually about 5 – 10 minutes in Big results 8length.

  • 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.Big results 10

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?Big results 11
    • 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!

Reggio-Inspired Mathematics in Surrey

Over 125 Primary Teachers from Surrey gathered on Thursday, January 28, 2016 in our new Resource and Education Centre (REC) to explore and discover elements and ideas of1 Reggio-Inspired Mathematics.  Many teachers have become more aware of the highly regarded early learning program from Reggio Emilia, Italy.   In Surrey, there is a growing interest in how Reggio-Inspired practices might enhance mathematical teaching and learning. After teaching all day, these teachers eagerly explored direct provocations focusing on Number, Pattern, Geometry and Measurement.  There was enthusiasm as they used ‘loose materials’ and ‘mathematically structured’ materials to investigate the mathematics.

2We explored the practices that would help develop our students’ mathematical understanding:

  • To see the image of the child as capable and creative, and responsible for their own learning
  • To create an aesthetic environment that is a place for wonder
  • To focus on the ‘Big Ideas’ and an emergent curriculum
  • To use ‘loose parts’, nature and mathematically structured materials to build understanding
  • To use documentation to make learning visible3

The role of the teacher was discussed:

  • To create an inquiry based environment
  • To listen and ask questions
  • To ‘toss the ball’ back to students
  • To help students uncover the curriculum
  • To document the learning
  • To e4na5ble students to build on their understanding

Bringing the outdoors indoors is an important principle of Reggio.  Children are so interested in learning through nature.  Providing natural materials for 6the students to explore mathematics increases engagement and wonder.  Mathematically structured materials like pattern blocks, ten frames and Cuisenaire rods are often provided to discover concepts.

With the revised curriculum it is so important that teachers have a deep understanding of mathematics.  Janice Novakowski and myself have created ‘concept’ summaries for essential understandings involving; Subitizing, Counting, Patterning and Place Value.  These often help teachers to build on their own understanding of the concepts.7

Teachers explored and made connections to the revised curriculum by focussing
on ‘Big Ideas’, curricular competencies, and content.  The idea of ‘Direct prompts,
Implied prompts and Open exploration’ was investigated during the session.

T8hanks to all the amazing teachers that attended the session.  Hopefully, you took away some ideas to use in your classroom.  Remember the important message… ‘One
Step at Time’!

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.

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Read a Story, Explore the Math

I feel honored to have spent time with over 90 amazing Primary teachers at the BCPTA conference in beautiful Victoria B.C. on October 24, 2014. What a wonderful group of dedicated teachers who love to learn some different ways to support their learners.

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Everyone loves a good story. Teachers love reading them and students love hearing them. What better way to set the stage for a math lesson. Last May 2014 Carole Fullerton and I collaborated together to create a new resource Read a Story: Explore the Math. IMG_7014

This resource promotes the teaching of important math concepts through the exploration of delightful children’s books. Many of these books are newly published and all have the potential for students to engage in math and provide opportunities to explore in meaningful ways.

IMG_1618At the conference we shared most of the books, some of the activities and tried a few for ourselves. We explored the tasks with Cuisenaire rods, dominoes, two sided counters, ten frames and dice. By using the manipulatives the students are encouraged to make connections to the concepts and represent their thinking in concrete ways.IMG_0980

Stories allow us a shared experiences. They engage us emotionally, and make us curious about the world. Carole and I hope that this resources will provide ideas for possibilities to pair stories with mathematical investigations that will inspire rich mathematical thinking in your students.

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Basic to the Basic ~ A Better Way – Part 2

Report cards, snow, flu and tired bodies didn’t stop over 50 teachers from attending the second part of ‘Back to the Basics’.  It always amazes me that these dedicated teachers attend after school workshops to network, share and learn together.  Thank you all for caring so much about your students and helping them to make sense of mathematics.  We all agreed that we want our students to understand the basic addition and subtraction facts by applying strategies that make sense.  Please continue the conversations and building the important foundation with our young learners.

part 2

Now I Know My ABCs

blog post by Lillah Martin

This afternoon over 70 teachers gathered to hear Sandra and I talk about the basics of teaching the alphabet.  Most children come into our classrooms “knowing” the alphabet because of the ABC song, or TV shows that showcase the alphabet but they do not have an alphabet awareness that makes sense to becoming writers and readers.  We have many little learners that think “lmnop” is one “thing”!

We revisited a very old program based on Anna Ingham’s blended sight sound method, with some adaptions of our own, and shared a story for all 26 letters, that gave the explicit sound as well  the letter formation. Using this “method”, the letters are introduced in groups of 2 or 3, selected by the way they are voiced, common usage, or sometimes the shape they have.  We spent time noticing where the tongue is in relation to the roof of the mouth, or the teeth, what shape the lips take and analyzing how the sound “feels”.   Many children need to have this pointed out to them.  The letters are introduced quickly, explicitly, and with an engaging little story that the children can easily remember .

Alphabet StripBy the nature of this method, all letters are introduced within a month, left on display, referred to in meaningful ways that build connections, allowing for each learner to take their next steps in a developmentally “makes sense” way.

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The “what next…” in the classroom was also shared with ideas for using children’s names, alphabet books and  embedding letters/sounds at every opportunity.  With small group explicit instruction and meaningful activities to target specific  areas you will see a joyful explosion of confident writers and readers.

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The alphabet song does still have a very important place in our classroom—it should be visible in the room and sung at least 3 times a day as it lists the letters in order, is a great strategy tool for learners to go to when they are looking for a letter they need BUT every time it is sung, someone needs to be tracking and touching the letters in the song.  Sing it fast, sing it slow, sing it high, sing it low, sing it with stops at specific letters, and try to sing it using the sounds.  Play with it asking questions like “how many letters have holes in them, straight lines, or curvy lines?”  Notice which ones are tall, which ones hang down, which ones are in your name, your friends name, which ones “are easy for you” etc.  Make it so familiar that all learners feel success with the 26 keys to our language!

Back to the Basics – A Better Way

Pic1Another amazing group of over 70 primary teachers met after school to learn more about teaching the ‘Basic Addition and Subtraction facts’ in a meaningful way on February 12, 2014.  This was part one of a two-part series.  I am always so thrilled to see the dedication of hard working, caring teachers who want their students to truly make sense of mathematics.

It is so important for the students to establish a firm foundation of ‘Number Sense’ before teachers start presenting strategies to help students understand the facts.

We know that students still need to “know their facts”, however, memorization and timed drills didn’t work for many students (and still doesn’t).  Some of our struggling mathematicians have been drilled for years and still struggle as they enter high school. .  A structured, thoughtful and systematic approach is required for all students to build understanding, fluency and application of the basic addition and subtraction facts.  Teachers need to provide ‘direct instruction’, guided practice, and then independent practice. The concept behind the ‘gradual release of responsibility’ is so important in providing the opportunity for all students to build understanding.

Many of the ideas presented are taken from Carole Fullerton’s resources.

Mastering the Facts SubtractionNumber SenseMastering the Facts Addition

“Mastery of the facts is very different from memorization of them.  Mastery depends on the co-existence of overlapping competencies as shown in the following diagram…”

VennDiagram

“Promoting these competencies through direct instruction, rich tasks and meaningful practice will allow our learners to truly master the facts.”                                                            Carol Fullerton, 2012

Let’s provide the opportunity for all students to build a strong understanding of the basic addition and subtraction facts.  Stay tuned for Part 2!