Blog - Creating a path

Maths - Where do our problems lie?

3/14/2019

Our next round is at Granville East and we hope to deepen our understanding about how to teach and lead so that our students can think like mathematicians.

Our blog is started by Nicki from GEPS. She writes:
According to Di Siemon, Number is routinely identified by teachers as the most difficult aspect of school mathematics to teach and learn....and differences in performance are almost entirely due to difficulties with larger whole numbers and related concepts such as multiplicative thinking. Do you agree? What makes you say that?

Louise Reynolds

3/15/2019 02:51:34 pm

Nicki - I would agree. Number seems to be such a deep concept that has big conceptual ideas organised layer-upon-layer-upon-layer!! Whereas some aspects of mesurement, (let's take Area) seem to be smaller concepts.
My wondering was: Is it enough to develop deep understandings in number - or do you need to develop understanding across the strands? I think you need both - but number is more foundational and impacts on the diversity of elements of maths.

Nicki

3/18/2019 04:28:48 pm

It is great to read the comments and wonderings here. There is certainly much to think on! I certainly agree with Faye, that language is critical, and must be embedded in the teaching of mathematics (both technical language and meta-language).

In preparation for this rounds I have been challenged by Di Siemon's "lines in the sand" that need to be drawn, determining the mathematical understandings that are non-negotiable, rather than 'mile-wide' but 'inch deep' syllabus coverage. There is also the issue of teachers deeply understanding the concepts but at the same time recognising that they cannot be simply taught. Rather, students need to construct these understandings through multiple experiences that are designed by the teacher.

I think these mathematical understandings need to be developed around number, which underpins other strands, together with the working mathematically concepts - in particular reasoning. When we can reason with number, we can apply our understandings to solve number problems in the real world. It seems to me that many other mathematical concepts from other strands, such as area (for example) are examples of reasoned number theory that are commonly used in daily life (ie extension of mulitplicative thinking). Does this make sense to others?

Barbara

3/16/2019 09:29:21 pm

Thanks Nicki & Louise for starting our thinking about this week’s round. Yes, I believe all the strands are important We all need to be able to measure accurately and to have concepts of shapes, Understanding of statistics and probability is essential in our age of information. However, I think concepts of number are core – they underpin the concepts in the two other two strands. They are the most important aspects of maths for the early years.
It seems to me that misunderstandings about number are more frequent with students, and more difficult to remediate. If a Year 6 student doesn’t understand what a parallel line is – then maybe a lesson or two can fix that. But if a Year 6 student doesn’t have a sound sense of how the number 6789 could be deconstructed, or understand which is greater 0.04 or 40%, then there’s a whole lot of learning needed going back to the foundations.
In our Di Siemon reading, a study is cited that shows that there is an 8-year range in achievement in Number for each school Year 4 – 8. And finds this discrepancy is unacceptable in a country that prides itself on our education. Jo Boaler, in the chapter, “Creating Mathematical Mindsets” says “number sense is the foundation for all higher level mathematics” (p36). She states that in the USA and similar countries students have been introduced to algorithms for adding, subtracting, multiplying & dividing numbers by the age of seven. Because of this many students early experiences of maths is one of confusion ,where they gain a strong belief that maths is all about instruction and rules. (pp1&2). And if these are mindsets that students develop, then incorrect application of these rules can happen often. You can see a great illustration how this looks in the short comedy video clip, 5 x 14 = 25 on "Our Next Round" page.
Just as in the video, it is often the case the case that students’ misunderstandings feed upon themselves until maths in its entirety is one enormous unsolvable puzzle? I was at a café recently, splitting the bill amongst friends. When we asked what the bill would be the waitress just stood there perplexed and, after a long pause, called out to others in the café, “Does anyone know maths?”
So, my questions to you are: How do we ensure that our students develop number sense? How do we foster the KLA knowledge of our teachers so they are presenting maths in a way that ensures conceptual development, not just a list of instructions and rules? And how do we ensure, in our school’s curriculums, that our students develop deep understandings of the really key concepts that will be needed for future learning, rather than shallow understandings of the overwhelming amount of content that is our state curriculum?

Diane

3/17/2019 10:25:05 am

How do we ensure that our students develop number sense?
I believe number sense mainly involves the strategy of finding new facts based on facts students already know. In saying this, the number sense questions need to be open enough to target our students of varying abilities and allow students to realise that there are multiple ways to obtain an answer. In ES1, at the beginning of term, I presented students with 6 dots and asked them “what do you see?”. Ss responded with “circles” “dots” and counting with 1:1 and then saying “6 dots”
When presenting the same six dots during term 4 most students could instantly see 6 dots without counting, other responses included “3 and 3 makes 6” “2,4,6”, “2 groups of 3”, “3 groups of 2”.
I believe, a number a talk a day has helped to build number sense, especially when students try to use the strategies they had seen from the previous day.

How do we foster the KLA knowledge of our teachers so they are presenting maths in a way that ensures conceptual development, not just a list of instructions and rules? And how do we ensure, in our school’s curriculums, that our students develop deep understandings of the really key concepts that will be needed for future learning, rather than shallow understandings of the overwhelming amount of content that is our state curriculum?
From my readings and PL, teachers need to understand that it is not our teaching program that determines the pace of our lessons. There is no point in teaching addition and subtraction, if they can’t count in sequence or have correct one to one... right? Teachers need to expose students to on stage content but once that’s done, we need to really consider the individual needs of our students. According to mathematics consultant, Anita Chin, The mathematics syllabus is a developmental sequence- therefore, it is a good guide for teachers to know where to step back or step forward to help drive the learning forward. A teacher in stage 1, should also have a good understanding of ES1 content to help “fill in the gaps”. They should also have an understanding of stage 2 content for those extension students. Anita Chin mentions “when teachers know their content well, lessons become more flexible, making it easier to differentiate.”

Fay

3/18/2019 03:20:48 pm

At BPS like everywhere else we need to start with our context. Burwood Learners need explicit teaching, scaffolding and support to develop their knowledge and deep understanding of the language of mathematics. Without the appropriate metalanguage students cannot reason, communicate substantively or demonstrate their understanding of key mathematical concepts.
Often, our learners can perform mathematical operations however struggle to identify the embedded mathematics in number problems.

Yes we agree that number is the most difficult concept to teach and learn, and within the context of Burwood it is important to teach the demands of language in conjunction with number sense.

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Maths - Where do our problems lie?