Tag Archives: numeracy

Early Numeracy: Mathematicians at Play

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“Problem solving is natural to young children because the world is new to them & they exhibit curiosity, intelligence & flexibility as they face new situations. The challenge … is to build on children’s innate problem-solving inclinations & to preserve & encourage a disposition that values problem solving.”

• Principles & Standards for School Mathematics

 

We want all children to see themselves as confident and competent mathematicians. They need to be able to explore ideas, solve problems and communicate their thinking. Mathematics continues to be a barrier for some struggling learners and we recognize that early intervention is the key to improving outcomes. The Early Numeracy Teacher (ENT) position has been developed to support these learners in the Early Years.

The Early Years are a time for exploring – for play, talk and investigations. Our youngest learners come to understand key concepts through their play. They spontaneously explore mathematical concepts through activities that are engaging and encourage them to think. The ENT works collaboratively with the classroom teacher to scaffold, discuss and develop the students’ deep understanding of important mathematical concepts.

In 2014-15 Early Numeracy Teachers will provide support to kindergarten and grade one students in 13 elementary schools. It is based on a collaborative model between the ENT and classroom teacher to provide in-class, targeted small group instruction, through meaningful engaging activities.

Early Numeracy Teachers are trained in current research and pedagogy on early learning and numeracy, under the guidance of Sandra Ball, one of our district Helping Teachers. They are also trained in the use of assessment tools such as the early numeracy “What Do They Know?” (WDTK). Classroom teachers and Early Numeracy teachers work collaboratively to assess what the students know (a strength based model) and develop instructional strategies to support the learning.

In order to be successful in the early years, students need to demonstrate capacity in three areas of numeracy: subitizing (the instant recognition of a quantity), partitioning or decomposition (the ability to break apart a number and put it back together again), and patterning (the ability to recognize, represent and describe repeating patterns with different attributes). These are the main concepts that the ENT will focus on with our ‘at promise’ students.

Early numeracy support has been provided to schools for three years. Comments from teachers indicate the importance and value this work has had for learners and for their own growth as professionals.

The Perspective of Early Learning Teachers:

“Most importantly I have seen the importance of ‘not teaching the intuitive knowledge out of students’ while developing our young mathematicians. The role allows students the time and space to invent and play with their own strategies, permitting a more flexible rather than rigid approach to numeracy, and they begin to show a more in-tune understanding of math concepts because they were personally involved in the making-meaning process.” 

“It is imperative to ‘catch them when they’re young’.  I have discovered that children as young as kindergarteners can do the work of a mathematician if they are given that mindset. They are most proud of their work when you tell them they are ‘being’ mathematicians and ‘thinking’ like one.  I have learned that there are three basic fundamental concepts that form the foundation which leads to understanding.  By focusing on these three areas, I have found that ‘at promise’ students have the capacity to become confident learners in numeracy.  In the process of ‘doing’ math, they are also developing a positive attitude, bringing much joy and excitement to the tasks as I hear them express:  ‘I’m good at this game, I love Math. It’s so much fun, I wish we could do Math all day.’  I have learned that generally it takes ‘at promise’ students longer to grasp concepts, but when you present the concepts through the use of many different game formats and interesting hands-on manipulatives, they stay actively engaged.   They often surprise you with their thinking and understanding, and I have had the privilege to be present to share in their thinking, see where they are struggling, and to celebrate their successes. …They begin to see relationships between numbers and patterns and they become more flexible in their thinking and problem solving.  Part of my role is to help these students see themselves as capable learners.”

The Perspective of Classroom Teachers:

ENTPic1“Working with the ENT has made me a much more confident math teacher. The program has encouraged us to stay focused on math at certain set times during the week. The students look forward to the hands on/tactile activities and games each week. I love how we can focus on small groups and tackle different learners in different ways. Over the past 2 years we have created so many stations/games for the students to use. They want to go to those stations even when it isn’t math time.”

The Perspective of a Principal:

A principal describes why she felt the early numeracy support was beneficial to her school:
• The ENT develops positive, trusting relationships with staff and students over time
• Students change perception and self-confidence in numeracy and are more positive “Math is fun!”
• Working collaboratively with classroom teachers over time to model best practice and expose highly engaging activities, resources and manipulative strategies for teaching
• There is easier transfer of number sense, patterning, etc. understanding to classroom lessons

The role of the ENT is to work collaboratively to support students who need to build their confidence, competence and disposition of mathematics. The redesigned mathematics curriculum emphasizes problem solving. Just as there is more to literacy than teaching the rules and procedures of language, there is more to numeracy than teaching the rules and procedures of mathematics. Numerate individuals not only “know” mathematics, but also understand it in personally meaningful terms. They feel competent and confident about their ability to draw on the necessary knowledge and apply it in new and relevant ways. The results we have collected over the last few years strongly support the importance of this work for our ‘at promise’ mathematicians.

Note: Karen Alvarez (@_alvarez_k) District Principal (Early Learning, Literacy, Fine Arts) and Sandra Ball (@SandraBall1), our Early Learning Inner City Helping Teacher, co-authored this post. A wealth of resources and examples for supporting Early Learners can be found on Sandra Ball’s website (see here). For more information on Numeracy projects in Surrey Schools, including a program review, check out this tab.

The Real Flip: Where Students do the Math

Bill Gates dismisses it – this belief that children can construct their own understanding of mathematics. Many educators disagree.

John Van de Walle’s student-centred approach? Marilyn Burns’ insight into how children learn math? The rationale in the WNCP curriculum? The beliefs of the BCAMT? Gates would dismiss them all.

More importantly to me, he would dismiss the successes that Surrey teachers and students experience when teachers let go and give students a chance to do the math. “Letting go” does not mean students are left to discover the Pythagorean Theorem on their own. The role of the constructivist teacher is to get students mentally ready to work on a task, listen, provide hints, and facilitate discussion.

Instead, Gates supports the Khan Academy and the flipped classroom model. In this model, students watch a video at home so that they can get one-on-one homework help at school. Sometimes, flipping proponents claim that this model frees the teacher up to have students do real problem solving. With all the press that the flipped classroom is getting, there is surprisingly little anecdotal evidence of this actually happening.

Gates, Khan, and others have missed the point. Problem solving isn’t something you do after you have learned a concept. That’s practice. Students should solve problems not to apply but to learn new mathematics. The flipped classroom model removes teachers from the most important part of teaching – the introduction of new concepts.

Suppose the proverbial teacher across the hall doesn’t buy in to “all that constructivist stuff” and is considering flipping his or her classroom. Here are three questions that I would ask:

1. Does teaching = telling? (See how I made that a math question?)

I understand if the general public views teaching as simply delivering content, it’s probably what they experienced as learners. Teaching, like real estate, is one of those careers that everyone thinks they can do. I guess I expect my fellow educators to know better. I thought we no longer viewed children as empty vessels to be filled with knowledge. I thought we were moving away from seeing curriculum as topics to “get through.” I thought we were moving towards an emphasis on the mathematical processes. Earning badges online seems like a giant step backwards to me.

2. When you are explaining a new concept, is the interaction between you and your students important?

I have a confession to make. For most of my career, I have used a teacher-centred approach. Still, even in this traditional lecture format, students were given opportunities to ask me clarifying questions or check their understanding with a neighbour. I was able to pick up on subtle non-verbal cues and adapt my lesson on the fly. Throughout my career, all of my attempts to improve my teaching have me moving towards a more student-centred approach, not searching for a more efficient way to deliver a lecture.

3. How does replacing a one-size-fits-all lecture with a one-size-fits-all video meet the needs of all of your students?

 Flipping proponents exclaim, “Kids can pause and rewind videos! They can watch them over and over again!” Yeah. But it’s still the same video. This reminds me of the time I was lost in Naples. I asked a local for directions to the train station. He patiently repeated, in Italian, the directions to me several times. I was still lost. Last year, Dr. Marian Small spoke with almost 100 secondary math teachers from Surrey about differentiating instruction. Surrey teachers are beginning to use her two core strategies: open questions and parallel tasks. The ultimate goal of differentiation is to meet the varied learning needs of all students, not to have students complete a series of videos at their own pace.

My final objection to the flipped model is that it is being held up as revolutionary. Assigning a video lecture for homework, and then working on 1 to 49 odd in class instead of watching a lecture in class, and then working on 1 to 49 odd for homework should not be considered a revolution in math education. (If this flip did result in higher scores on standardized tests, does it matter?) We know that real change is difficult. Flipping a classroom isn’t – all that is needed is a tablet PC.

I would like to redefine what flipping a classroom means. My idea of a flipped classroom would be one in which students, not the teacher, are doing the math. Instead of teacher-created videos, the tools of my flipped classroom would be chart paper, felt markers, and sticky notes.

Technology will also play a role. In Surrey, secondary science/math teacher Blair Miller uses video, in the style of Dan Meyer, to ask engaging questions. His students use Vernier Video Physics, an iPad app, to analyze functions. His students interact with dynamic applets that he has created using GeoGebra.

These are effective uses of technology. This is a revolution that I can get behind.

 
Special thanks to Numeracy Helping Teacher Chris Hunter for this post. You can visit his blog at http://reflectionsinthewhy.wordpress.com/ or reach him at @chrisHunter36.

Want to learn more? Chris recommends the following:

• The Wrath Against Khan: Why Some Educators Are Questioning Khan Academy by Audrey Watters
• Khan Academy and the Mythical Math Cure by Sylvia Martinez
• Khan Academy: My Final Remarks by Frank Noschese
• Khan Academy Does Not Constitute an Education Revolution, but I’ll Tell You What Does by Steve Miranda
• Khan Academy Is Not the Progressive Model You Are Looking For by Tom Barrett
• It’s a Video Library, Not a Revolution by Diana Senechal
• Content Delivered, Captain. Full Speed Ahead by SD36 Helping Teacher Amy Newman