Back to the Basics – A Better Way

Another 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.

“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…”

“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!

Putting It All Together ~ Using Big Books and Pocket Charts ~

In the 70’s Don Holdaway developed the ‘Shared Reading’ strategies, which combined the powerfully positive context of bedtime/lap story reading with literacy instructions designed to promote active problem solving.  According to Holdaway, in a shared reading experience, there is a bonding between the expert and novice readers.

Shared reading is an important component of any primary classroom.  It involves:

• Read-along reading
• Whole group activity – text seen by all
• Modeling
• Consolidating emerging reading strategies
• Re-reading independently

The benefits of ‘Shared Reading and Writing’:

• Experiencing the joy of reading
• Drawing attention to the details of the text
• Providing systematic and explicit instruction
• Children see themselves as readers and writers

Lillah and I thought it was time to rejuvenate the ‘Shared Reading and Writing’ practices of the past.  We used ‘big books’ and pocket charts all the time with our students. They are excellent tools to develop early literacy skills, engage students in meaningful text and explore language in playful ways.  The journey from a ‘big book’, to a pocket chart, to independent writing is one that will help many children learn to read and write.  Check out your libraries to find the shared reading materials and bring them into your classrooms.  Enjoy and have fun together with your students.

‘Even the most generous lap cannot hold 20 children, so big books were created.’

Daily Math Investigations Part 2

Daily Math Investigations Part 2 took place in Surrey on November 21, 2013.  Around 70 dedicated teachers left their classrooms and report card writing (some very eager for a break) to explore, discover, share and network together.

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

The focus of the session was on ‘Rich Routines’ from Daily Math Investigations.

Rich Routines are:

open-ended thinking tasks done in larger groups

more structured, but not boring

concepts worth revisiting

increase in complexity as they are explored over and over

active and engaging for all students

Rich Routines are questions/investigations posed during a whole group time.  We have suggested a variety of routines that are predictable in nature but are engaging and open-ended enough to meet the needs of all the students. Here are some of the routines we discussed from the resource:

• All About Number
• Cuisenaire Investigations
• Exploring the Open Number Line
• Exploring the 100’s chart
• Numbers of the Day
• Counting Collections
• Messing with Data
• Sort it Out
• Teeter Totter Tales

Check out the new Entry Tasks that were introduced at yesterday’s session.
Many of the tasks were taken from the Numeracy Centre Fun section of the blog.

Enjoy and remember to …

Get them engaged

Get them thinking

Get them reasoning

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.

Patterns, Patterns, Everywhere!

The capacity to pattern – to establish a pattern core, to repeat and name it – is an essential skill in mathematics learning.  Students who can pattern can predict what comes next with confidence.  They know that there is order – to the manipulatives they use, to the days of the week, to the sequences of their days.  The capacity to pattern is a necessary pre-requisite for success in algebra – to be able to predict ‘down the line’ is the foundation of algebraic thinking.  Students should be able to represent it in language and actions.  Students who are competent with patterning will be able to identify and correct an error in an existing pattern. Students should be able to extend a pattern off of both ends (beyond both the start and the end) and to represent it in language and actions.

Patterning with colour or another physical attribute is the precursor to skip counting. When students build patterns with a pattern core of 2 elements, the number of objects in their pattern increases by 2 each time. To find the total number, then students can skip count by 2’s.  In this way they follow a new pattern:  skip a number, say a number, or skip 1, say 2, skip 3, say 4 etc.  Skip counting requires sets of objects to be counted.  Success with skip counting depends on being able to subitize, and see groups at a glance.

Number Talks – Big Results in a Small Amount of Time

I am always amazed at the dedication teachers have to attend after school workshops to explore ways to support their students.  Over 90 wonderful teachers gathered together to learn about ‘Number Talks’ on September 26, 2013.

Number Talks is one of the powerful vehicles for helping students to reason with numbers and build a solid foundation for algebraic thinking.  Teaching mathematics as a sense-making process is important for students to understand the math they are doing.  Number Talks is a daily whole group activity that takes 5 – 10 minutes which involves the solving of mental math tasks.   They promote flexibility with numbers, shared learning and increased confidence.  The purpose of Number Talks is to help students develop computational fluency, as well as number sense. We discussed ways to incorporate Number Talks into classrooms and get ‘big results for a small amount of time’ for students.  Please view the presentation and attached resources to gain more information about this simple activity to include in your daily routines.

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.