There has been some debate recently around the notion of an ‘over-crowded curriculum’ in NSW. The mathematics K-6 syllabus with its 250+ pages may be one of the first documents to come under fire for having too much content. We have a very detailed syllabus that provide teachers with explicit and clear content for classroom instruction. However, although this document is helpful in explaining what students need to be able to do to attain outcomes, some see the amount of content as overwhelming. If we were to try to teach each dot point and outcome in isolation then yes, it is an almost insurmountable task, but there are ways to combat this.

One way is changing our view of how the syllabuses work and what the intention was in creating them. Schools are required to show evidence of how they are addressing outcomes in programs and through reporting mechanisms, however, it’s how we teach them that needs more focus. As mentioned by Dr Catherine Attard in her recent post about the challenge of curriculum she points out that the mathematics syllabus doesn’t need to be taught in separate concepts even though it is structured that way as “the content has to be organised in a logical manner”.

The growing interest in inquiry-based learning and STEM approaches to an integrated curriculum is one way that content and outcomes are being meshed together, making connections across science, technology and mathematics outcomes. The more you delve into the science and technology syllabus, the more mathematics you see. The references to using data to collect and report on investigations, and to units of measurement used in data collection make clear the connections to the mathematics syllabus. In fact, some of the content dot points are almost word-for-word identical, for example in the mathematics syllabus it states that students:

- represent given or collected categorical data in tables, column graphs and picture graphs

Then in the science and technology syllabus it states that students:

- use a range of methods including tables and simple column graphs to represent data.

So why teach them twice, in isolation? Other learning areas, like science and technology, provide the contexts for which mathematical concepts can be applied.

Making connections within the mathematics syllabus is also another teaching strategy to combat the idea that “there is too much to cover”. Mathematics itself builds on foundational skills in number, often referred to as Number Sense. Without number sense, many students will find it difficult to understand more complex concepts as there is no base knowledge to build on. When speaking to one of my secondary colleagues she talked about the importance of students having foundations knowledge of the four operations and fractions and decimals when starting high school, “the rest I can teach them!” (if needed, in a shorter time to catch them up). These foundational concepts should be given more time in your sequence of teaching, most other concepts build on, or from these.

Visualising the connections in mathematics as mind maps, flow charts, infographics, connected webs or networks (see example reference links at the end of the blog) can be a useful way to assist you in planning your teaching sequences and making connections clearer for students in your class. Here are a few ideas for the connections that can be made and therefore these outcomes can be taught simultaneously or at least in a sequential manner.

### Early Stage 1

#### Connecting whole numbers, patterns and algebra, 2D space

In Kindergarten students learn to count using concrete materials such as counters. You can introduce shapes when students are counting (such as pattern or attribute blocks) either as countable objects or to count the number of sides of each shape. This counting concept can also be linked to patterns as students start to make simple patterns with shapes e.g. square, circle, square, circle… Students can count the items in the pattern to identify there are “two shapes in my pattern”.

### Stage 1

#### Connecting addition and subtraction, patterns and algebra, area

In years 1 and 2 students develop additive strategies such as counting on from a number other than one, using doubles and skip counting to solve addition tasks. This same concept of skip counting also appears in patterns and algebra to introduce number patterns e.g. 2, 4, 6, 8… This understanding can then be connected to solving area tasks by skip counting the number of rows in an array or rectangle e.g. 4 rows of 2 can be counted as 2, 4, 6, 8. These additive strategies and patterns are a precursor to multiplicative thinking. You could therefore also add another orange dot for multiplication and division to this image.

### Stage 2

#### Connecting multiplication and division, volume, 3D space

Building on from the connections made in Stage 1, by year 3 and 4 students are developing multiplicative ways of working with numbers as efficient strategies for solving tasks. Students can use knowledge of known multiples such as 2s, 5s and 10s to solve tasks that involve multiple layers in volume questions. For example, when creating a prism with a volume of 20 blocks students may think of the prism having 2 layers and therefore divide the 20 by 2, 10 blocks in each layer, so one layer will be 2 x 5. This activity brings together 3D space and volume and applies multiplication and division in a real-world context.

### Stage 3

#### Connecting multiplication and division, fractions and decimals, area

In year 5 and 6 students extend their understanding of find areas of shapes by exploring triangles. For students to develop understanding they need experience with physical manipulatives (e.g. paper or string to make triangles by halving rectangles or squares) so that using the method of halving the base then multiplying by the height makes sense. This connects to the Stage 3 concept of finding fractions of whole numbers and provides examples of when it is used. Using area for explaining the concept of multiplying and dividing by fractions is also vital. This allows students to build a visual concept of the act of operating with fractions and builds on the Stage 2 concept of using the region model to solve multiplication tasks and to represent fractions

Making connections allows students to see the interrelatedness of mathematical concepts and provides space for them to apply number concepts in other areas. Regarding “content to cover”, I’d like to shift the focus from seeing content and outcomes as things to cover to seeing the content as ways to address the outcomes. Cover tends to lead teachers to see the dot points at boxes to check off, whereas address gives the dot points a purpose- they are there to help. The syllabus places this upfront in the organisation of content page where it states:

“The content describes in more detail how the outcomes are to be interpreted and used, and the intended learning appropriate for the stage”.

The content helps you interpret what the outcome is all about. The syllabus also goes on to state that:

“In considering the intended learning,

teachers will make decisions about the sequence, the emphasis to be given to particular areas of content, and any adjustments required based on the needs, interests and abilities of their students”.

I’ve highlighted the part of the sentence that I think gives power to the classroom teacher where YOU are the decision maker about the sequence and emphasis given to content. For example, a ‘teach a concept a week’ scope and sequence makes it difficult for teachers to be flexible within their classroom instruction when making these types of decisions that best suit their students’ needs, interests and abilities.

I do not see our curriculum as overcrowded. Full, yes. Explicit, yes. But not overcrowded, what would you leave out? I think we can take a look and prioritise specific outcomes and concepts our students need more time with, and integrate outcomes where possible with other learning areas e.g. science and technology. I believe a larger issue at hand at present is the lack of time to teach the curriculum as the school week becomes overcrowded by extra-curricular activities, but that debate is for another blog post!

#### Resources

Visualising the connections in mathematics as:

- Mind maps by Cathy Fosnot in Creating the conditions for learning mathematics
- Connected webs by Jo Boaler in Tour of mathematical connections and What is mathematical beauty?
- Networks by Lynne McClure in Underground Mathematics

#### References

Board of Studies, NSW. (2012). *Mathematics K-10 syllabus* retrieved from

http://syllabus.nesa.nsw.edu.au/mathematics/mathematics-k10