Blog - Creating a path

Mathematics - A balancing act?

7/27/2018

2016 mathematics became whole school focus because results showed a gap between English and maths achievement.  The first IR rounds supported this decision. Data indicated that there is a mismatch between the confidence of our students and their mathematical skill.  Our kids love maths and think they are good at it, but NAPLAN results indicate a majority of our students in years 3 and 5 are not ‘Proficient’ in numeracy (they are not in the top 2 NAPLAN bands).

In 2017, TEN training K-2 was implemented to improve teacher understanding of the continuum of learning in mathematics and highlight the importance of establishing strong foundational skills in numeracy.  Positive feedback from the teachers has seen a modified form TEN training being implemented with 3-6 teachers in 2018.

As a result of 2017 IR findings and recommendation the whole staff created a vision for mathematics at OGPS. We held a twilight session and asked our staff where to next? This process indicated that many of our teachers had the strong belief that students need the "basic skills" before they are able to/or given the opportunity to attempt working mathematical tasks. Therefore we changed the focus of our PL to collaboratively in stage teams design and implement tasks where students had to use mathematical reasoning. Teams shared their tasks and what they'd learnt from them at a whole school staff meeting. The purpose behind this was to show that our students ‘can do it’ if given the opportunity. As a result each stage now has a working mathematically focus.

In 2018 OGPS has been working with Anita Chin to strengthen staff understanding of the mathematics syllabus and the language of maths K-6.  We want to understand how students progress from K to Year 6 -not just within a stage.  This will lead to the development of a refined whole school scope and sequence.

Some questions that we are still considering are:
How do we get a balance between teaching the skills and providing opportunities for students to apply their skills in open ended problem solving situations?
How do we successfully incorporate working mathematically into the TEN framework?

Barbara

7/29/2018 06:17:37 pm

Hmm Interesting question. I'm thinking that it all should be quite seamless. I'm wondering how teachers see teaching the skills? Are there opportunities for students to experiment, communicate with other students and use a variety of methods.

Here's a link to an interesting article by Jo Boaler about the difference between high achieving and low achieving students in mathematics. https://www.youcubed.org/resource/number-sense/

The main difference is that high achieving students interact with numbers flexibly and conceptually. I wonder whether the different mathematical mindsets of teachers have created this difference?

Number Talks, advocated by Boaler, seems to me to be a really worthwhile strategy for our maths classes. Have other people seen this in action?

And is changing the teachers' mindset about maths a critical factor? And if so, how do we do that?

Maddy

8/2/2018 08:55:43 pm

I found the article by Jo Boaler very interesting and relevant. It made me really think about my students at the moment and how they engage and interact with numbers. Using TEN in my classroom it allows me to explicitly teach students the fundamental skills of number, addition and subtraction for problem solving. I am able to teach various strategies that students can use to solve addition and subtraction problems. But I wonder...Am I giving them the opportunity to take risks in their learning and to experiment with various number problems and to choose their method of solving the problem?

Sharen Scerri

7/30/2018 10:59:38 am

Yes Barbara, K-2 staff have been discussing number talks for a while now & their potential impact on developing & refining number sense. Stage 1 have implemented informal number talks into our introductory section of number lessons & this term are introducing a literature-based, conceptual focus during allocated "Maths Literacy" times. Through the library we have purchased a wide range of quality literature with a maths theme (covering many strands) which we have used to develop a teacher-modelled read-aloud /number sense program to be implemented across our seven stage 1 classes. Our four ES1 classes have integrated number talks into their number programs.
Continued discussions with teachers about the importance of students' flexible use of a wide range of operational strategies & recognising what students need to move beyond count-by-one strategies, especially older students, is vital to widening teachers' perceptions about our students as learners of maths. The use of mixed-ability grouping to develop WM outcomes is another important consideration for our teachers. In fact, should we be working with mixed-ability groups across skill lessons in number also? Research supports mixed-ability groups so it's something worth considering.

Louise

8/1/2018 10:31:57 am

Amanda, Zeinab and I have just had a fabulously intense conversation prompted by the comment about skills and applying them should be seamless.

We realised that we were all using different understandings about what problem solving is (we called it little "p" and big "P" problem solving!!).

We've decided that problem solving happens WHILST you are teaching new concepts - eg, discussing and using what they already know whilst they are learning new big ideas - justifying and reasoning around the new concept and using games as ways of stimulating conversations about their thinking - as it is developing.

We focused on the pivotal role of the teacher. It is our job to activate student thinking and links from old to new knowledge; and help them grow their number sense in a variety of ways and contexts. The teacher can name and notice thinking and ways the students' thinking can be applied to content areas.

Next week, Stage 3 are learning about decimals, as our assessment showed they didn't understand the actual concept of a decimal - let alone which place value means what!!
So - the teachers will be going back to some conceptual understandings of whole numbers, using a number line. Students will be doing a number talk about 1.8 - what do you know about it? What else? What else?

Students will be comparing decimals; placing them on number lines; using whiteboards to play decimal games; problem solving around ordering numbers and justifying responses. All of this will be loud and messy and the teacher will be carefully listening to student's conceptual thinking in order to scaffold them forwards.... (there will be more - we've only just started planning!!).

SO - we think that teachers can teach students skills and concepts whilst having students apply their knowledge every day!

about our differing understandings

Burwood PS

8/2/2018 03:12:56 pm

In preparation for creating the pre-task, we had a lot of discussion around the importance of communication in the maths classroom. In our context we have a strong EAL/D focus and we believe teaching maths vocabulary is as just as important as teaching English vocabulary. We believe the same approach should be used to teach maths vocabulary in order to deepen student understanding. Students need to be able to apply the vocabulary when solving open ended maths questions.
Teachers should provide opportunities for students to talk, explain, argue, justify and discuss ideas in mathematics in order to promote creative and critical thinking skills. Our aim is for our students to use these skills in the real world.

Barbara Reynolds

8/2/2018 06:49:22 pm

Love your thinking Burwood PS. It makes sense that teaching vocabulary for maths is just as important as teaching vocabulary for English. You might like this blog from Mark Chubb, "The smallest Decisions Have the Biggest Impact". (https://buildingmathematicians.wordpress.com/2017/01/15/the-smallest-decisions-have-the-biggest-impact/)

It starts with a series of questions:
- Who gets the most time to talk?
- Do you show first or allow students to make sense first?

And then discusses in depth a dilemma about when to introduce scaffolding? We give teachers a lot of guidance about the importance of scaffolding. But when do we introduce it in the lesson? And if we're over-scaffolding are we preventing our students from moving to the "goldilocks" zone - a place where they are challenged?

8/2/2018 08:31:18 pm

Another great blog post by mark chubb!
A great example about scaffolding (using 3 - 9 examples of cubes) and that the small decisions we make often show what we value (ie struggle, order).
I also liked the table about teacher belief, focus area and methods. If you see basic skills as the focus then you’re more likely to skill and drill based on model & practice at diff levels.
However, if your beliefs are about constructivist theory then your focus is on students constructing knowledge, so you’re more likely to design investigations where students are guided to create mathematical understandings as they do/act/try and then articulate culminating knowledge.
It comes back to teacher mindsets and the fact that little decisions in a lesson can reveal and change the learning.

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Mathematics - A balancing act?