Maths and Climate Change
"The only constant in the world is change." said an ancient sage, Lao Tse.
Change happens constantly in our lives. These changes impact our lives in different ways. Climate change is no different. Some natural changes to climate, however, inevitably will happen. But changes due to man’s actions such as human economic activities can be mitigated and their effects minimised by humans themselves. This is the focus of this project, that is, to find out what activities cause and affect climate change and then suggest possible changes to these human activities by adopting and adapting best practices to achieve better sustainable human progress.
There are 3 goals for this project: The first goal is for students to be able to search, analyse, interpret and appreciate mathematical data to better understand climate change and assimilate its understanding into their lives. It is hoped that this will help them understand the gravity of the global problem and appreciate suggestions to adapt positive changes in their lifestyles and habits. The second goal is for students to implement activities to disseminate their findings, experiences and share insights with their immediate local community as well as the bigger global community, thus, creating climate change awareness and meaningful practices. The third goal is to be able to refute or accept with reasons skeptical views regarding climate change.
Students play the role of an ecologist to investigate from various sources how climate changes are taking place worldwide. They will search for evidence that show unnatural and unusual changes: changes that result from immoderate human activities. They will analyse algebraic and statistical data obtained from technological media and use tools like emission calculator, GPS, etc. They will set up an online forum, a special interest group and use Google documents and other web 2.0 technologies such as wiki and blog to collaborative with and get contributions from experts from local and global communities.
In a school forum, students will present their findings as ecologists using PowerPoint presentation and other modes. This forum will include teachers and students from various disciplines. They will then publicise their findings in brochures and publish their results on a website. They brainstorm to suggest practical ways on how the local citizens can help reduce climate change and prevent global warming. Finally, they will assess various supporting and skeptical views regarding climate change, and, hopefully, will arrive at a logical conclusion based on reasons about climate change.
The proposal report /letter will be sent to the Head of State / Minister of Environment. Further copies will be sent to the local press. Since climate change and global warming are global issues, the findings will be disseminated on global platforms online.
The students will be assessed and evaluated using checklists and through weekly self-reflective postings in their blogs. They will also be evaluated during their involvement in activities in publicizing their findings in brochures, publishing in a website and writing the report/ letter to the PM / Minister and press.
- Essential Question:
How do we live with change?
- Unit Questions:
How does climate change impact our daily life?
How can Mathematics help us understand significant changes that are taking place in climatic patterns?
How can we help to minimize the impact of climate change in our lives and the environment?
- Content Questions:
What is climate change?
Where do we find quantitative data & empirical evidence of climate change?
How do we use this data to visualise and show climate change?
How can we make a comparative study of natural causes as opposed to man-made causes of climate change?
What are some suggested best practices to reduce climate change?
What other steps can we take to help prevent global warming?
What are some sceptical views regarding climate change?
How can we disseminate the knowledge, experiences and insights resulting from this study to the public, locally and globally?
From your study how badly is the world affected by climate change, considering evidence that support and those that refute this claim?
How can we live responsibly by accommodating to climate change?
Initially, a K-W-L Chart will be used to assess students’ prior knowledge of climate change and what kind of mathematical tools can be employed in making an in-depth study of this topic.
Various assessment tools are used throughout the project to monitor students’ progress. These assessments help students keep on target and self evaluate their accomplishments. They also help teachers to ensure the set goals are achieved, apart from monitoring students’ progress. They also provide feedback on the processes, performances, and products. Reflection on learning throughout the project is encouraged through a blog.
Questioning is used throughout the unit to help students develop their higher-order thinking skills and process content as well as to monitor learning. Students use various checklists to help them guide their learning, stay on track, and self-assess their progress.
Assessment takes place daily, based on daily observations and student products. Individual and group conferences are held often to help monitor progress and answer any quires. The project rubric is used to self- and peer-assess work prior to completion. This project rubric is also used to assess and grade final presentation and completed project.
A Blog site will be used to help students provide feedback and for teachers to monitor students' progress while a wiki site will be used for group members to collaborate and discuss issues online.
Teacher sets up a group site at http://engage.intel.com/groups/climate-change with relevant assignments and resources such as the video-clip from YouTube* for this project. Teacher also sets up a blog site for student reflection and feedback at http://maths-and-climate-change.blogspot.com* and a discussion site at http://maths-and-climate-change.wikispaces.com/* which also includes instructions for students.
Teacher follows the schedule as in the implementation plan (doc).
Begin the unit by asking the Essential Question: ‘How do we live with change?’
Open discussion: Introduce the following Unit Question: ‘How does climate change impact our daily life?’ Explain to the students that they will be exploring answers to this question on most parts of their project work. To assess students’ prior knowledge about climate change a short discussion is held using the K-W-L chart (ppt).
To further inspire and motivate students to take some positive actions on the current issue on climate change a video-clip from the Internet: http://www.youtube.com/watch?v=zzjOcOcQ90U* (2.02 minutes) is viewed and a general discussion follows on “What difference would you make?”
Begin the project by using the multimedia presentation (ppt). Show possible effects of climate changes like melting ice shores and mountain ice caps, rising sea levels, floods, tsunamis, heat waves, etc. Brainstorm possible topics related to these phenomena. Seek out possible data sources, both qualitative and quantitative evidences that may link between these phenomena and climate change. Information links are provided such as the Copenhagen Conference and the Kyoto Protocol, including those on a blog (doc).
Discuss and evaluate the ideas students contribute. Ask if statistical analysis using Mathematical modeling would be appropriate for the topics suggested. (Careful guidance is necessary to help students pick projects for which Mathematical modeling is appropriate.) Discuss print and electronic resources for collecting data. Possible topics include:
- Water resources
- Forest resoruces
- Coastal resources
- Ocean and Fisheries
- Food securities
- Sea levels, depleting ice shores and residing mountain ice caps
- Energy resources and heat generation
- Human settlements and impact on the environment
- Natural disaster sites: tsunami, earth quakes, cyclones, volcanic eruptions , floods, landslides
- WHO: Health, birth, mortality, diseases, life span
- UNPD, etc
Hand out the project rubric (doc) and discuss. The rubric provides an overview of the project expectations for the students. Have students use the rubric to help them assess their progress and learning.
Students get into teams taking specific roles as such an oceanographer, geologist, climatologist, ecologist, WHO director, Minister of Health, and other relevant roles to seek out evidence. Student role may change if there is a need and be best supported by acceptable reasons. Each team will only explore one topic listed above.
Week 1 will be the time when each student will maintain their reflection on a Blog * evaluating what they have learnt from the topic and their personal thoughts about the climate change issue.
Students discuss the Unit Question: "How does Mathematics show climate change?” and the Content Questions: "Where do we find quantitative data & empirical evidence of climate change?" and "How do we use this data to visualise and show climate change?"
Exhibition forum: During this forum, student teams prepare initial chart paper and post them at their own station in the classroom. Have student team members take turns to mend the station answering questions that explore the Unit Questions in their expert role capacity when other students come a visiting. Tags are worn to identify their roles.
Tell students that they will create two projects - One offline and one online. They will incorporate answers to the Unit Question that was introduced on Week 1, ‘How does climate change impact our daily life?’ and Unit Questions on Week 2, ‘How does Mathematics show climate change?’ What climate changes are the results of natural causes and what are man-made causes, and how do we show this, if possible?’
The projects are:
- A multimedia presentation about the impact of climate change.
- A bulletin board with brief articles and graphs about possible effects and implications of climate change using mathematical tools of statistical analysis
- A wiki * is used by the students to set-up a web-site about the topic, including implications and effects (The wiki should include data or a graphical representation of data to back up any predictions.)
- A forum (doc) (on same wiki) where team member invite members from the community and discuss the issue
Students are already in their teams as in Week 1. Remind students to use the Unit Questions in their projects.
Hand out the slideshow checklist (doc) and the bulletin checklist to all students during the exhibition forum. After that the forum / wiki checklist (doc) can be distributed. Review the checklists and have students use them to monitor their progress while working on the project.
They are told to work on these two online and offline projects until completion on Week 7 when their presentation will be made in a “Summit on Climate Change”.
Students begin researching their topics. Teacher conferences with students individually and as teams to answer questions, discuss their progress, and assess higher-order thinking. This will be done through the blog, wiki and face to face sessions. Students will also use google.documents to share files and collaborate ideas online.
The focus will be on the Wiki and Forum maintained to collaboratively work and find answers to the Unit Question: “What climate changes are the results of natural causes and what are man-made causes, and how do we show this, if possible?”
Engage them to reason out why certain causes are difficult to be differentiated.
Show students how to do Mathematical modeling and explain the following mathematical terms:
- Linear and non-linear functions
Students create equations of curve of best fit using their own data. Allow students to choose either their graphing calculator or a spreadsheet to enter data. If they choose the spreadsheet, have them examine the data graphically that best fit their data, allowing them to make reliable predictions. Next, have students calculate future predictions and they can use the principles of extrapolation.
Whatever progress that they make, they will post their findings, discussions, conclusions and even problems that they face on their Wiki and Forum. They are told to maintain the spirit of truthfulness and transparency in their project.
Students create graphs of historical data versus curve of best fit and brainstorm the ramifications of predictions. Provide students with time to complete additional research as needed.
They will try to explore answers to this Unit Question: “How can we live responsibly by best practices in response to climate change?” and the Content Question: “What are some suggested best practices to reduce climate change?”
Students complete the research on their topic using the links provided, incorporating their mathematical knowledge. They will keep updating their findings in their Wiki and Forum.
Introduce the Question: "How do we evaluate various views in support of or which oppose climate change?" and "What are some sceptical views with regard to climate change?"
Students will complete their PowerPoint presentations, their Wikis and personal Blogs. The forum now will be used only if they are still issues to be discussed.
The students are reminded that their collaborative team Wikis may be different from their own opinions posted in their personal Blogs. Noting the differences will help students live a life skill in accepting differences, besides living with change.
A “Summit on Climate Change” is held to table and present various positions in regard to climate change. The students will then review their own research and findings with that of other teams. Brochures are handed out during the summit.
Remind students to use their checklists to review and finalize their work.
Students present their final projects to the upper secondary class students from Form 4 and Form 5. Use the scoring guide (doc) to assess students’ work.
In their presentation, students would have provided answers to the following questions
- What is climate change?
- What or who causes climate change?
- What does Mathematics data say about climate change?
- How can we help to minimize the impact of climate change in our lives and the environment?
- In what ways can we adapt to change?
- What skeptical views are reasonable and what are not, supported by reasons and data, if possible.
All the teams will collectively agree on the most important points from their research, findings and collaboration as a class (or United Nation’s!) decision, if possible. They will come up with ways to publicise their findings in brochure, publishing in a class website and writing the report/ letter to press.
If they can’t come to a consensus, which will most probably be the case in reality, then what compromise should be adopted?
- Experience using graphing calculators, spreadsheets
- Experience creating graph by using technology tool
- Experience using graphing calculators, spreadsheets
- Familiarity with conducting Internet research
Special Needs Students
- Reduce assignments or allow more time as needed
- While grouping students, ensure those with special needs are grouped with high and average ability students so that they can peer-coach while carrying out activities.
- Additional graphic organizers can be made available for these students.
- Have the student create a linear function for the same data, compare it to the exponential function, and then answer the question, which function is more realistic and why?
- Gifted student are given the task of leading the group in carrying out various activities.
- They can be assigned the task of peer-teaching to help other group members to acquire skills such as computer or Internet search skills.
- They can be assigned task of creating a web site
- Allow the student to access Internet sites in the student’s first language
- Pair the student with a peer
The team members that put this project idea together were Mr. Teoh Boon Tat, Dr. Warabhorn Preechaporn & Dr. Leong Chee Kin (Mathematics Education Specialists from SEAMEO RECSAM). Other teachers expanded on the initial idea as developed here.
At a Glance
Year/Form: Form 4 / 5
Subject(s): Mathematics, Science, Social Science & Moral Education
Topics: Maths & Climate Change
Key Learnings: Algebraic & Statistical analysis in climate change
Time Needed: 8 Weeks (2 hours per week)