Selection of Math Labs

compiled and created by Shawn Urban

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What are Math Labs? | Samples of Math Research Projects and Labs | Math Labs Online | Alberta Curriculum Outcomes | References

*Profound mathematical ideas [and activities] are often embedded in deceptively simple questions [and tasks].*
— Dan Finkel

Alberta Education has joined NCTM and the Western Provinces of Canada in updating it K-12 mathematical sciences curriculum. The emphasis this round focuses on learning math through problem solving, rather than learning math for problem solving and learning about problem solving (Scammell 2010). Students need to understand the Math they are working on, rather than just do the math they are working through. For example, students now need to understand and explain what tangent and secant functions are; it is no longer enough to just be able to solve tan(θ) = O/A and sec(θ) = H/A. This means they must know why tan(θ) = O/A and sec(θ) = H/A and how and why the measure of a tangent function differs from that of a tangent line, and similarly the same for a secant function and a secant line.

**Math labs** are designed to provide students with the opportunity to use and experience Math. Unlike a series of rote math questions, **Math labs** are rich extended tasks which challenge students to spend more time to investigate a math problem and to actively attend to and reflect on the Math they are working on while and following the activity they engage in in response to the task.

*Note the distinction made between math and Math (Pimm 2006 and Papert 2012; notation by Pimm). This is explained further in Math Labs 2 and 4.*

Engag-in' Math Labs

© Shawn Urban 2012. CC BY-NC-SA 4.0

Here are some original and minimally modified Math lab tasks. Dr. David Pimm of the University of Alberta used, and probably created, many of these in his EDSE 439 (Problem Solving and History in Mathematics) and 540 (Exploring Tasks and Texts) courses. Dr. Pimm meant these to be used in the classroom, so feel free to use, bank and share them so long as proper credit is included in the tasks.

- Incomplete Tasks and Conscious Activities (Pimm 2006)
- Exploring History and Posing Problems (Pimm 2006)
- Curriculum Archaeology (Donald 2006)
- Sealed Mystery Math Task (Pimm 2006)
- Strange Dice (Urban 2005)
- All-digits Arithmetic (Urban and Coble 2014)
- Logic and Calendar Construction (Urban 2012)
- Error in Mensa (Urban 2016)

More Math Labs and Rich Maths Online

- Awesome Math Tasks
- CT4ME - Math Projects
- Exeter Academy Math Teaching Materials
- Galileo Educational Network Association - Math Investigations
- John Golden's Blog - Math, Game Design and Teaching
- John Golden's Blog - Math Games
- KenKen - Puzzles that Make You Smarter
- Masters of Many Theorems
- Math 4 Love
- Math is Fun - Math and Logic Puzzles
- Math Project Journal - Lesson Plans and Articles
- Math Projects for Science Fairs
- MathGuide - Math Projects
- Mathematics Task Center - Hands-on Problem Solving
- NCTM - Problem to Ponder
- NCTM - Standard 1: Worthwhile Mathematical Tasks
- NRICH - Specialists in Rich Mathematics
- NRICH - Weekly Challenge
- NRICH - Weekly Problem
- Ole' Miss Math Challenge
- Project Euler
- Rich Tasks
- UKMT - UK Mathematics Tournament
- Yummy Math
- Google "Interesting Math Task"
- Google "Math Investigations"
- Google "Math Lab Activities"
- Five Triangles Mathematics
- 7 Puzzle
- 365 Things to Make You Go Hmmm
- Math Book Makeover Workshop

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Math 20-2 and 30-2 Mathematics Research Projects (Alberta Education 2015)

General Outcome: Develop an appreciation of the role of mathematics in society.

Specific Outcomes: It is expected that students will research and give a presentation on a historical (20-2) or current (30-2) event or an area of interest that involves mathematics.

Mathematical Processes: Visualization, Mental Mathematics and Estimates, Problem Solving, Reasoning, Connections, Technology, Communication

ICT Outcomes:

C1 – Students will access, use and communicate information from a variety of technologies.

4.2 select information from appropriate sources, including primary and secondary sources

4.4 communicate in a persuasive and engaging manner, through appropriate forms, such as speeches, letters, reports and multimedia presentations, applying

information technologies for context, audience and purpose that extend and communicate understanding of complex issuesC2 – Students will seek alternative viewpoints, using information technologies.

4.1 consult a wide variety of sources that reflect varied viewpoints on particular topicsC3 – Students will critically assess information accessed through the use of a variety of technologies.

4.1 assess the authority, reliability and validity of electronically accessed information

4.2 demonstrate discriminatory selection of electronically accessed information that is relevant to a particular topicC7 – Students will use electronic research techniques to construct personal knowledge and meaning.

4.2 analyze and synthesize information to determine patterns and links among ideasF2 – Students will understand the role of technology as it applies to self, work and society.

4.7 use current, reliable information sources from around the world30-2 only

P2 – Students will organize and manipulate data.

4.1 manipulate and present data through the selection of appropriate tools, such as scientific instrumentation, calculators, databases and/or spreadsheets

Achievement Indicators: The following set of indicators may be used to determine whether students have met the criteria above.

- Collect primary or secondary data (statistical or informational) related to the topic.
- Assess the accuracy, reliability and relevance of the primary or secondary data collected by:
- identifying examples of bias and points of view
- identifying and describing the data collection methods
- determining if the data is relevant
- determining if the data is consistent with information obtained from other sources on the same topic.
- Interpret data, using statistical methods if applicable.
- Identify controversial issues, if any, and present multiple sides of the issues with supporting data.
- Organize and present the research project, with or without technology.

References

Alberta Education. (2015). Mathematics, Grades 10-12. Edmonton, Alberta: Crown in Right of Alberta.

Brown, S.I.; and Walter, M.I. (2005). The Art of Problem Posing. Third edition. Mahwah, New Jersey: Lawrence Erlbaum Associates, Inc.

Donald, Dwayne. (2006). Personal communication. EDSE 500 (Introduction to Curriculum Studies). Edmonton, Alberta: University of Alberta.

Flewelling, G.; and Higginson, W. (2000). A Handbook on Rich Learning Tasks. Kingston, Ontario: Center for Mathematics, Science and Technology Education, Queen's University.

Harnasz, Costel. (1994). Do you need to know how it works? Selingel, M. (Ed.) Teaching Mathematics. London, England: Taylor and Francis(Routledge). pp. 137-144. – an exemplar of a mathematics history (Napier's bones, slide rules, a seventeenth Century English math dispute).

Pimm, David. (2006). Personal communication. EDSE 439 (Problem Solving and History in Mathematics) and 540 (Exploring Tasks and Texts). Edmonton, Alberta: University of Alberta.

Prestage, S.; and Perks, P. (2001). New questions for old. Adapting and Extending Secondary Mathematics Tasks. London, England: David Fulton Publishers. pp. 18-30.

Scammell, John. (2010). Personal communication. Learning Math THROUGH Problem Solving. Online 11/24/10: Edmonton Regional Learning Consortium.

Urban, S. (2005). Personal Communication. Strange Dice. Edmonton, Alberta: University of Alberta.

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