Guest post from Dr Pip Arnold: Pip is an accredited PLD facilitator and a member of the AMA executive. The ideas in this post are from Pip’s perspective and experiences and may not represent the views of others on the AMA executive.
“One of the guiding principles of the New Zealand curriculum is coherence, whereby students are offered “a broad education that makes links within and across . learning areas” (Ministry of Education, 2007, p. 9). When used effectively, curriculum integration provides a learning environment that offers this coherent education, allowing connections to be made within and across subjects (Beane, 1997; Etim, 2005; Fraser, 2000; Murdoch & Hornsby, 1997).”
Read more from Deborah Fraser on curriculum integration
Over the last three years a lot of the work I have been doing with schools, teachers and students has involved working with mathematics departments and primary teachers to integrate mathematics and statistics across the curriculum.
Below are some of my current thoughts and links to a few New Zealand and overseas resources. This is by no means an exclusive list. Get in touch if you have examples to share
The schools have used different models of integration, including:
- Pairing of subjects across year 9 and 10. Two teachers from different subjects develop a term-long programme that integrates the learning outcomes from the two subjects. Teachers deliver the programme together in combined/shared spaces.
- Schools having a theme for a term and all subjects linking into the theme. This can be more formal connections across subjects e.g. the mathematics teacher working with the science teacher.
- Primary teachers connect mathematics and statistics with other curriculum area(s) for a short or longer period of time.
I have come to the conclusion that integration works best when the mathematics and statistics integration is authentic and allows for deep learning of the mathematics and statistics. At this point in my journey I think the connections or integration come from two perspectives.
The first perspective is where the two (or more subjects) have a strong achievement objective integration or alignment. In this perspective there are two ways this can happen.
- Either mathematics and statistics achievement objectives work as a support or tool for the other curriculum area. For example
Science objective: [Material world level 1 & 2] properties and changes of matter where students learn to observe, describe, and compare physical and chemical properties of common materials and changes that occur when materials are mixed, heated, or cooled.
Mathematics and statistics objective: [Geometry and measurement Level1] Order and compare objects or events by length, area, volume and capacity, weight (mass), turn (angle), temperature, and time by direct comparison and/or counting whole numbers of units. In this case the mathematics and statistics learning is supporting the science through the required measuring skills needed to learn about properties and changes of matter.
- Or the mathematics and statistics and the other curriculum area achievement objectives are aligned.
Mathematics and statistics objective: [Statistics Level 2]. Conduct investigations using the statistical enquiry cycle: posing and answering questions; gathering, sorting, and displaying category and whole-number data; communicating findings based on the data.
Science objective: [Understanding about science Level 1 and 2]. Appreciate that scientists ask questions about our world that lead to investigations and that open-mindedness is important because there may be more than one explanation. In this case an investigation (that is most likely a science context) allows students to develop skills in conducting investigations using both science and statistics skills and knowledge.
The second perspective is where the connection is solely by the context rather than integration as described in the first perspective. For example the context used for mathematics and statistics can connect to the other curriculum area achievement objective, but the mathematics and statistics is not acting as a support nor is it aligned.
In one school the theme for the term was identity. In religious education students explored their spiritual identity, in social studies they explored where they come from and their cultural identity. A “context” link for mathematics was to explore mathematical identities. In this example the mathematics connection is to identity but not in the sense that the religious education or social studies achievement objectives are.
Whichever perspective you take to integrate the mathematics and statistics it is important to go deep and develop conceptual mathematical and statistical understanding. Other things to consider include:
- You will not get curriculum coverage through integration, be ok with this
- If students have choice of modules/kete/courses then they will only do some elements of the curriculum, be ok with this
- You need to be flexible, generally the mathematics and statistics is easier to integrate/align with other subjects if you are flexible and are prepared to do the mathematics/statistics that aligns best rather than your next “topic”, then everyone will realise that mathematics and statistics rocks and is everywhere
- Not everything in mathematics and statistics integrates easily with other curriculum areas, this is ok. Take some time to develop your mathematical and statistical “toolbox” instead but this is not an excuse to not to try integration
- Have fun, look at your students interests, your interests. What hooks your students into the learning?
New Zealand based resources
nzmaths has a series of ready to go units from Level 1 to Level 4 that are linked to other curriculum areas as well as mathematics and statistics. View them here .
Also on nzmaths is Thames High school’s story which shares how over the last three years they have developed and refined their local curriculum to contain a mixture of core subject time, cross-curricular kete and high interest projects. Have a browse through the list below to see a snapshot of how they are doping things.
- Physical education and statistics (curriculum level 4, summary and bivariate situations) – Crunch the coach
- Art and mathematics (curriculum level 4, transformation geometry) – Tessellations, Transformation and Art
- English and mathematics (curriculum level 5, trigonometry) – Goodnight stories for builders and architects to be
- Physical education and statistics (curriculum level 5, comparative situations) – The Numbers Don’t Lie
- Fabric technology and mathematics (curriculum level 5, transformation geometry, circles, nets) – Transforming shapes
- English and mathematics (curriculum level 5, location and bearings) – Never get lost
- Food technology and mathematics (curriculum level 5, proportions and measurement) – Mocktails
Zac Rutledge from Thames High School, also shared their story through AMAonline in Term 2. In this session Zac talked us through their three year journey as they transitioned from a traditional model to a cross-curricular model in the junior school. He said while they found the transition challenging, they have done lots of learning along the way. Watch the recording of the session share in their journey and learn from their success and failures along the way. Resources from the session can be found here
Other AMAonline sessions that focussed on integrated learning include:
- Linking Digital Technologies to mathematics where Tracey Pacheco, Blend Learning, shared how we could make links between the computational thinking strand of Digital Technologies within the technology curriculum area and the mathematics curriculum and how we could incorporate this in the classroom.
- Creating a school where streaming is not necessary. Francis shared Inglewood High School’s journey and the experiences of teachers and students on the impact removing streaming and changing the way they approached learning in Year 9 and 10 from a ‘traditional’ programme to one offering more choice and flexibility. Resources from the session an be found here
- Integrating mathematics and statistics within NCEA at level 1 and 2. In this session Andrew shared the experiences of Rototuna High School around integrating mathematics at NCEA level 1, and 2. Examples included Mathematics and PE, Mathematics and Chemistry, Mathematics and Music, Mathematics and Food Technology.
Over the past couple of years teachers have shared how they are connecting with other curriculum areas at Statistics teachers day. Here are three resources from the sessions that are on Census at School
- Cross curricular projects to give meaning to statistics, Abigail Mantaj. Abigail gave a snapshot of Howick College’s journey putting together a statistics, science (sustainability) and English project for Level 2. She showcased student work and gave a quick fire quiz on NCEA rules around internal assessments. She shared her thoughts about other internal standards that fit well and could be assessed together. The teachers followed the learning journey of Year 9 and 10 community action students (who learn social studies and statistics at the same time) by looking at an old set of data with a new pair of eyes!
- Authentic connections – using mathematics and statistics in other learning areas The team from Mission Heights Junior College, Chandana, Tashi, Meera, shared how they stepped “outside the bounds of curriculum areas” (Sandretto, 2012, p. 3) and away from an “orthodox curriculum focus” (Hipkins, 2012, p. 2) – this investigation at its heart is based on the premise of using curriculum areas other than mathematics as an authentic context for integrating statistical and probabilistic concepts (our initial starting point), and supporting teachers to think outside the box of the formal curriculum subject demarcations and moving away from a strictly mathematics focus. This workshop shared the teaching/learning experiences, from within the classroom, which have resulted from this project.
- Innovative cross-curricular assessment In this session Subash Chandar, Vimal Sighn, Kathryn Albertson from Ormiston Senior College presented a workshop on innovative cross-curricular assessments. At level 1, the statistics team and PE teachers worked on 91035, Investigate a given mulitvariate data set, and at level 2. they combined questionnaire design with Business studies. At level 3 the department moved away from traditional reports to presentations and posters for assessment.
Other New Zealand sites worth exploring when you get a chance for ways to integrate mathematics and statistics with other curriculum areas include:
- The Great NZ NCEA Hackathon 2020 is a Facebook group for New Zealand educators wanting to develop and share ideas for delivering creative and connected NCEA tasks that allow students to gather evidence for multiple standards whilst working remotely
- NZTA have written units of work that can be used with minimal changes
- Auckland Museum at home
The following list of websites are ones that I have used to provide ideas for integrating mathematics and statistics with other curriculum areas.
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See the latest Concord Consortium newsletter here.
Oceans of Data
The Oceans of Data Institute (ODI) is dedicated to transforming education to help people succeed in school, work, and life in a data-intensive world. We envision a world where everyone has the skills and knowledge to make informed decisions and achieve new insights and understandings using data.
Explore the K-16 projects on the ODI website for many examples of integrated units with data. Check out the resources for example, Ocean Tracks: High School Learning Modules | Oceans of Data.
World’s largest lesson
The World’s Largest Lesson promotes the use of the Sustainable Development Goals in learning so that children can contribute to a better future for all. From citizenship and justice to climate change and the environment, inspire children to make a difference!
This platform brings together resources, case studies and background information to help teachers and other educators bring a global dimension to their work. Link to the mathematics specific area of the site is here.
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Photo by Waldemar Brandt on Unsplash