Math walk

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A math walk, or math trail, is a type of themed walk in the US, where direct experience is translated into the language of mathematics or abstract mathematical sciences such as information science, computer science, decision science, or probability and statistics. Some sources specify how to create a math walk [1] [2] whereas others define a math walk at a specific location such as a junior high school [3] or in Boston. [4] The journal The Mathematics Teacher includes a special section titled "Mathematical Lens" in many issues [5] with the metaphor of lens capturing seeing the world as mathematics.

Contents

Informal learning

The idea that "math is everywhere", which is emphasized on a math walk, is captured by the philosophy of mathematicism with its early adherents, Pythagoras and Plato. The math walk also implicitly involves experiencing math via modeling since mathematics serves to model what we sense. [6] The math walk is a form of informal learning, [7] often in an outside environment or in a museum. [8] This type of learning is contrasted with formal learning, which tends to be more structured and performed in a classroom. [9] Math walks have been shown to encourage students to think more deeply about mathematics, and to connect school content to the real world. [10]

Maps and object discovery

There are different approaches to designing a math walk. The walk can be guided or unguided. In a guided walk, the learners are guided by a person knowledgeable in the topic of mathematics. In an unguided walk, learners are provided with a map. The map identifies walking stops and identifiers, such as QR codes or bluetooth beacons, [11] [12] to provide additional information on how the objects experienced during a math walk are translated into mathematical language. [13]

Example math walk scene

A walk can involve translation only, or translation and problem solving. For example, considering a window on a building involves first perceiving the window. After perception, there is a translation of the form of the window to mathematical language, such as the array where is the window's width and is the window's length. The array is a mathematical model of the window. This modeling is pure translation, without explicit problem solving. Questions such as "what is the area of the window?" require not only translation, but also the problem of solving for area: . [14]

Railroad tracks and other objects comprising part of a math walk in Fernandina Beach Historic District. Railroad Tracks Fernandina Beach.jpg
Railroad tracks and other objects comprising part of a math walk in Fernandina Beach Historic District.

A photo of the railroad tracks in Fernandina Beach Historic District captures a stop on a math walk. The walk's information can focus on discrete items. These items reflect counting and number sense. [15] Examples of discrete items are the cloud structures, the distant red harbor cranes, power line poles, wooden railroad ties, the diagonal lines in the road, and the cross walk across the rails. [16]

The counting of the ties leads to the idea of iteration in computer programming and, more generally, to discrete mathematics, the core of computer science. For iteration, we can use a programming language such as Python or C to encode the syntactical form of the iteration for a computer program. [17]

Other computer science related topics include a labeled directed graph that defines a semantic network. [18] Such a network captures the objects in the photo as well as the relations among those objects. The semantic network is generally represented by a diagram with circles (concepts) and arrows (directed relations). There are additional indirect mathematical relations, including a differential equation that would define the motion of the train engine, with time as an independent variable. [19]

Connecting school subject to standards

Exemplars of informal learning, such as a math walk, create opportunities for traditional education in school. Math walks can be a component in classroom pedagogy or in an after-school event. A key strategy is to create a mapping from what is learned on the walk to what is learned in school. This task is complicated due to geographic region, classification, and standards. A math walk can be situated as early as elementary school. [20] [21]

The map to disciplinary subject area in US Math Education begins with the majority of states having adopted Common Core, which includes English Language and Mathematics. Within each state's standards, one must identify the grade level. [22] A table in Common Core, titled "Mathematics Domains at Each Grade Level" summarizes the mapping of math subject to level. Once the mapping is known between object on the math walk and corresponding school subjects, this mapping should be included as part of the walk information. This linkage will assist both student and teacher. "Know your audience" is key to the successful educational delivery along a math walk. [23]

References

  1. ↑ Wang, Min; Walkington, Candace; Dhingra, Koshi (2021-09-01). "Facilitating Student-Created Math Walks" . Mathematics Teacher: Learning and Teaching PK-12. 114 (9): 670–676. doi:10.5951/MTLT.2021.0030. ISSN   0025-5769. S2CID   239668375.
  2. ↑ Druken, Bridget; Frazin, Sarah (2018). "Modeling with Math Trails". Ohio Journal of School Mathematics. 79 (1).
  3. ↑ Lancaster, Ron; Delisi, Vince (1997). "A Mathematics Trail at Exeter Academy" . The Mathematics Teacher. 90 (3): 234–237. doi:10.5951/MT.90.3.0234. ISSN   0025-5769. JSTOR   27970118.
  4. ↑ Rosenthal, Matthew M.; Ampadu, Clement K. (1999). "Making Mathematics Real: The Boston Math Trail" . Mathematics Teaching in the Middle School. 5 (3): 140–147. doi:10.5951/MTMS.5.3.0140. ISSN   1072-0839. JSTOR   41180762.
  5. ↑ "The Mathematics Teacher on JSTOR". www.jstor.org. Retrieved 2023-02-21.
  6. ↑ Adam, John A. (2009). A mathematical nature walk. Princeton. ISBN   978-0-691-12895-5. OCLC   263065394.{{cite book}}: CS1 maint: location missing publisher (link)
  7. ↑ The necessity of informal learning. Frank Coffield, Economic and Social Research Council. Bristol: Policy Press. 2000. ISBN   1-86134-152-0. OCLC   43745963.{{cite book}}: CS1 maint: others (link)
  8. ↑ Dauben, Joseph; Senechal, Marjorie (2015-09-01). "Math at the Met". The Mathematical Intelligencer. 37 (3): 41–54. doi: 10.1007/s00283-015-9571-8 . ISSN   1866-7414. S2CID   253814473.
  9. ↑ Malcolm, Janice; Hodkinson, Phil; Colley, Helen (2003-01-01). "The interrelationships between informal and formal learning". Journal of Workplace Learning. 15 (7/8): 313–318. doi:10.1108/13665620310504783. ISSN   1366-5626.
  10. ↑ Wang, Min; Walkington, Candace (2023). "Investigating problem-posing during math walks in informal learning spaces". Frontiers in Psychology. 14. doi: 10.3389/fpsyg.2023.1106676 . ISSN   1664-1078. PMC   10027002 . PMID   36949919.
  11. ↑ Burns, Monica (2016). Deeper learning with QR codes and augmented reality : a scannable solution for your classroom. Thousand Oaks, California. ISBN   978-1-5063-3176-8. OCLC   950572027.{{cite book}}: CS1 maint: location missing publisher (link)
  12. ↑ Cirani, Simone (2018). Internet of Things : Architectures, Protocols and Standards. Gianluigi Ferrari, Marco Picone, Luca Veltri. Newark: John Wiley & Sons, Incorporated. ISBN   978-1-119-35968-5. OCLC   1051140308.
  13. ↑ Scheinerman, Edward R. (2011). Mathematical notation. [United States]: [CreateSpace]. ISBN   978-1-4662-3052-1. OCLC   776864462.
  14. ↑ Bender, Edward A. (2000). An introduction to mathematical modeling. Mineola, N.Y.: Dover Publications. ISBN   0-486-41180-X. OCLC   43616065.
  15. ↑ Humphreys, Cathy (2015). Making number talks matter : developing mathematical practices and deepening understanding, grades 4-10. Ruth E. Parker. Portland, Maine. ISBN   978-1-57110-998-9. OCLC   898425070.{{cite book}}: CS1 maint: location missing publisher (link)
  16. ↑ Crouzet, Sébastien; Serre, Thomas (2011). "What are the Visual Features Underlying Rapid Object Recognition?". Frontiers in Psychology. 2: 326. doi: 10.3389/fpsyg.2011.00326 . ISSN   1664-1078. PMC   3216029 . PMID   22110461.
  17. ↑ FIshwick, Paul (2014-05-18). "Computing as model-based empirical science". Proceedings of the 2nd ACM SIGSIM Conference on Principles of Advanced Discrete Simulation. SIGSIM PADS '14. New York, NY, USA: Association for Computing Machinery. pp. 205–212. doi:10.1145/2601381.2601391. ISBN   978-1-4503-2794-7. S2CID   16278369.
  18. ↑ Lehmann, Fritz (1992-01-01). "Semantic networks". Computers & Mathematics with Applications. 23 (2): 1–50. doi: 10.1016/0898-1221(92)90135-5 . ISSN   0898-1221.
  19. ↑ Coddington, Earl A. (1989). An introduction to ordinary differential equations (Dover ed.). New York. ISBN   978-0-486-13183-2. OCLC   829154337.{{cite book}}: CS1 maint: location missing publisher (link)
  20. ↑ Hale, Deborah (2017). Math Trails and Other Outside Math Aventures (1st ed.). Amazon, Inc. ASIN   B06WGTC6KB.
  21. ↑ Richardson, Kim Margaret (2004). "Designing Math Trails for the Elementary School" . Teaching Children Mathematics. 11 (1): 8–14. doi:10.5951/TCM.11.1.0008. ISSN   1073-5836. JSTOR   41198385.
  22. ↑ National Council of Teachers of Mathematics. Commission on Standards for School Mathematics (1989). Curriculum and evaluation standards for school mathematics. Reston, Va.: The Council. ISBN   0-87353-273-2. OCLC   19669578.
  23. ↑ Borich, Gary D. (2015). Observation skills for effective teaching : research-based practice (Seventh ed.). Boulder, Colorado. ISBN   978-1-61205-677-7. OCLC   878667494.{{cite book}}: CS1 maint: location missing publisher (link)
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