Making more room for mathematics

Kilpatrick, Swafford and Findell Adding it up

Just as reasoning is the glue that holds all mathematical concepts together, the general capabilities are the glue that hold the curriculum learning areas together. The general capabilities are a lens through which we can view the whole curriculum. When we talk about students’ having the necessary skills to be future- focused thinkers, problem solvers, 21st century learners- the general capabilities encapsulate what we want our students to be:

literate, numerate, creative, critical thinkers
able to use their information and communication technology capabilities to work collaboratively with others where their personal and social capabilities play a large role
empathetic, showing cultural and ethical understanding of others.

When our students have all of these aspects working together, they will become

“successful learners, confident and creative individuals, and active and informed citizens.”

ACARA

The general capabilities can assist in making connections across syllabuses and point to opportunities for integrated learning. The general capabilities are the lens and each learning area content provide the contexts. Numeracy links are tagged in each NSW syllabus (other than mathematics) and are sometimes only given a passing glance, ‘ticked off’ as completed in a program or listed at the beginning of a learning sequence. Numeracy is more powerful than that, it can assist in making more room for mathematics. If you are feeling that there is too much mathematics ‘to get through’ in your mathematics lessons, when you just want to be focusing more on the number concepts your students are yet to master, then this general capability is for you!

There are a number of sub strands of mathematics that lend themselves to be explored and consolidated within other learning areas during your teaching week. This can then free up your mathematics lessons for a stronger focus on number and algebra and linked concepts when needed. This is not to say do not teach measurement and geometry in mathematics, as connections across mathematical concepts are essential. However, if students do not understand foundation skills in number and algebra then their ability to succeed and become numerate may be inhibited.

“We need to trust in our professional judgement and we need to understand that it’s perfectly okay to take the time and ensure ALL learners understand what they need to before moving on to more complex and abstract mathematics.”

Dr Catherine Attard Improving primary mathematics: the challenge of curriculum

I’m thinking specifically of the example of being a year 6 teacher with students still using inefficient strategies for the four operations. I want to spend more time on developing these skills as they are foundational for understanding fractions, ratios, measurement and algebra etc. In this case, spending equal weeks or lessons on, for example, mass as multiplication and division in mathematics lessons, isn’t teaching to the student or their needs, it’s just ‘covering the content’.

As primary teachers we have the ability to be flexible, to teach aspects of English and mathematics in other areas. We generally do this well for English, choosing text focuses based on what we are currently addressing in HSIE or Science and Technology and linking these to our reading or writing sequences. Are we doing this for mathematics? Is any part of your mathematics scope addressed in other key learning areas? I know I am guilty in the past of standing near the school fence having students count car colours to make graphs in mathematics! Instead, I should have explored this concept in my HSIE sessions, where students could survey other classes about their travel or connections to other places to link in with inquiry questions in geography. This way I could have made more room for mathematics.

A quick use of the filter by general capabilities on the NESA site will assist you in finding these links to numeracy across the syllabuses that you can then utilise when teaching other learning areas. Here are a few examples of how to incorporate parts of your mathematics scope (outcomes) into other learning areas.

Teaching space, measurement and data skills in Science and Technology when collecting data and designing plans.

Science and Technology
Stage 1 Earth and Space
ST1-8ES describes some observable changes that occur in the sky and landscape

record the observable changes that occur in the sky and on the land
collect data related to short-term weather events and long-term seasonal patterns, to inform others using appropriate communication techniques

Mathematics
Stage 1 Data
MA1-17SP gathers and organises data, displays data in lists, tables and picture graphs, and interprets the results

gather data and track what has been counted by using concrete materials, tally marks, words or symbols
interpret information presented in data displays…

Science and Technology
Stage 3 Built Environments
ST3-14BE describes systems in built environments and how social and environmental factors influence their design

draw a plan of, or model, a built environment that includes a range of systems to meet the needs and wants of a specific group of users, eg shade for a playground

Mathematics
Stage 3 3D Space
MA3-14MG identifies three-dimensional objects, including prisms and pyramids, on the basis of their properties, and visualises, sketches and constructs them given drawings of different views

visualise and sketch three-dimensional objects from different views, including top, front and side views
reflect on their own drawing of a three-dimensional object and consider how it can be improved (Reasoning)

Applying fractions, patterns and time concepts to Music when creating music using knowledge of patterns and structure.

Creative Arts
Stage 3 Music
MUS3.2 Improvises, experiments, selects, combines and orders sound using musical concepts

to create new work and to notate as a means of recording and communicating musical ideas
exploring the relationship between musical symbols and sound

Mathematics
Stage 3 Patterns and Algebra
MA3-8NA analyses and creates geometric and number patterns…

identify, continue and create simple number patterns…
describe patterns using the terms ‘increase’ and ‘decrease’
create, with materials or digital technologies, a variety of patterns…

Developing and building decimal understanding, data and timing skills in Physical Education when exploring daily and weekly activities.

PDHPE
Stage 2 Health safe and active lifestyles
PD2-8 investigates and participates in physical activities to promote the benefits of physical activity on health and wellbeing

analyse patterns of physical activity over time using ICT tools to record and propose changes to daily routines to reduce sedentary behaviour and increase physical activity levels

Mathematics
Stage 2 Time
MA2-13MG reads and records time in one-minute intervals and converts between hours, minutes and seconds

solve simple time problems using appropriate strategies, eg calculate the time spent on particular activities during the school day
explore and use the various date input and output options of digital technologies (communicating)

Introducing mapping and locating skills in Geography when investigating local places.

Geography
Stage 1 Features of places
GE1-3 communicates geographical information and uses geographical tools for inquiry

investigate activities that occur within places, for example:
- discussion of why and how the spaces within places can be rearranged for different purposes eg street fair, school hall
- examination of why various activities in an area are located where they are eg school, shops

Mathematics
Stage 1 Position
MA1-16MG represents and describes the positions of objects in everyday situations and on maps

interpret simple maps of familiar locations and identify the relative positions of key features
interpret simple maps by identifying objects in different locations, eg find a classroom on a school plan map
describe the positions of objects in models, photographs and drawings

Applying spatial and proportional reasoning and sketching in Visual Arts when representing objects in art making.

Visual Arts
Stage 3
VAS3.1 Investigates subject matter in an attempt to represent likenesses of things in the world

seeks to make artworks, using various techniques such as proportion, perspective, composition, foreshortening
utilises different artistic concepts eg colour, tone, line, scale, abstract, and explores how these may be used in their interpretation of this subject matter.

Mathematics
Stage 3 Position
MA1-16MG represents and describes the positions of objects in everyday situations and on maps

interpret simple maps of familiar locations and identify the relative positions of key features
interpret simple maps by identifying objects in different locations, eg find a classroom on a school plan map
describe the positions of objects in models, photographs and drawings

Developing proportional reasoning and scaling skills in History when interpreting and creating timelines of people and events.

History
Stage 2 First contacts
HT2-5 applies skills of historical inquiry and communication

identify the original inhabitants of Australia and create a timeline indicating their longevity in Australia of more than 50,000 years

Mathematics
Stage 2 Time
MA2-13MG reads and records time in one-minute intervals and converts between hours, minutes and seconds

read and interpret simple timetables, timelines and calendars
read and interpret timetables and timelines
explore and use different notations to record the date (Communicating)
explore and use the various date input and output options of digital technologies (Communicating)

Taking a STEM approach to inquiry-based learning allows for integrating and embedding mathematics with science and technology. These links are deep, not bound by content alone, as they connect through the processes of these subjects: working mathematically, working scientifically and working technologically.

Mathematics
Length
MA3-3WM gives a valid reason for supporting one possible solution over another

select and use the appropriate unit and measuring device to measure lengths and distances
describe how a length or distance was estimated and measured (Communicating, Problem Solving)

Science and Technology
Working Technologically
ST3-5WT
plans and implements a design process, selecting a range of tools, equipment, materials and techniques to produce solutions that address the design criteria and identified constraints

Students produce solutions by:

developing a plan and specifications to guide production
using their plans and production sequence

Mathematics – other links
MA3-1WM communicating
describes and represents mathematical situations in a variety of ways using mathematical terminology and some conventions
MA3-2WM problem solving
selects and applies appropriate problem-solving strategies, including the use of digital technologies, in undertaking investigations

References

Kilpatrick, J. Swafford, J. & Findell, B.(eds.)(2001). Adding it up: Helping children learn mathematics. Mathematics Learning Study Committee: National Research Council.

https://www.australiancurriculum.edu.au/f-10-curriculum/general-capabilities/

2006 Creative Arts syllabus accessed from http://educationstandards.nsw.edu.au/wps/wcm/connect/b72e0bc0-201d-40f4-8aac-d91c072d8f3b/K6_creatart_uw_music.pdf?MOD=AJPERES&CACHEID=ROOTWORKSPACE-b72e0bc0-201d-40f4-8aac-d91c072d8f3b-lzihNIi on Saturday 3 November 2018

2012 Mathematics syllabus accessed from https://syllabus.nesa.nsw.edu.au/mathematics/mathematics-k10/ on Saturday 3 November 2018

2012 Science and Technology K-6 syllabus accessed from https://syllabus.nesa.nsw.edu.au/science/science-k10/outcomes/ on Saturday 3 November 2018

2018 PDHPE syllabus accessed from https://educationstandards.nsw.edu.au/wps/portal/nesa/k-10/learning-areas/pdhpe/pdhpe-k-10-2018 on Saturday 3 November 2018