Experiential learning and graphing calculators
This wiki explores some of the links between experiential learning and graphing calculators.
Memorial University of Newfoundland
2 Experiential learning
Experiential learning is learning by experience throughout a person’s everyday life (Neill, 2006). Experiencing what is being studied through a hands-on approach rather than learning about it through an indirect approach allows students to learn through experiential learning (Smith, 2001). Experiential learning can benefit teachers and students. It provides teachers with another view on how students think and learn. This enables teachers to further help students in learning and understanding the topic being studied (Reilly, 2009).
There are four categories of experiential learning styles. They include activist, someone who would rather experience learning by doing; reflector, someone who reflects on what they have learned through observation; theorist, someone who chooses to understand concepts, reasons, and relationships; and pragmatist, someone who experiments with things to see if they work (Atherton, 2009).
3 Graphing calculators
Graphing calculators are programmable calculators with a large display screen that can be used for graphing, solving equations, and many other tasks that involve variables (“Graphing Calculators”, n.d.). Teachers often incorporate the use of graphing calculators into their mathematics classrooms to help increase the opportunities for their students to learn topics that involve graphing and computing (Garofalo, Drier, Harper, Timmerman, & Shockey, 2000). Allowing students the opportunity to learn concepts through experience with the use of the graphing calculator enhances students’ learning by allowing them to see a visual display of the results on the calculator screen. It also gives them the chance to explore concepts themselves through experience (Doerr & Zangor, 2000).
4 Experiential learning and graphing calculators
Experiential learning is gaining knowledge and understanding through experience (Kolb, Boyatzis, & Mainemelis, 1999). Using graphing calculators in teaching and learning mathematics gives students a chance to learn topics through experience by using a tool that gives them a hands-on learning opportunity (Harry, 2000).
Many educators, such as those in the Departments of Education and Mathematics, have used technology as an approach to learning and teaching mathematics and science. They have enhanced learning by allowing students to complete activities using a hands-on approach (Harry, 2000). If technology is used appropriately in the teaching and learning environment, it can increase learning opportunities for its participants (Hussain & Adeeb, 2009). Incorporating the use of graphing calculators in math classrooms also gives students a chance to increase their learning and understanding of topics through active engagement (Goos, Galbraith, Renshaw, & Geiger, 2001). Learning mathematics using a hands-on approach, such as with graphing calculators and other pieces of technology for graphing, produces higher success rates, especially in performance on visual and graphing tasks, than without the use of such tools (Hollar & Norwood, 1999).
Information from the internet can be programmed into graphing calculators. This can also help enhance the learning environment by helping to improve students’ understanding. Students can therefore retain information longer through the hands-on approach involving web-based information on graphing calculators (Sabry & Barker, 2009).
Not all students learn the same. Visual learners can benefit from graphing calculators. Theories of multiple intelligences and learning styles support the idea that some students may develop a better understanding of concepts when given the chance to use graphing calculators to explore mathematics (Simundza, 1995). Graphing calculators also enable students to gain a better understanding of problems using graphs, equations, and tables (Hollar & Norwood, 1999). The advantage of using the graphing calculator for these types of problems is that it provides a visual display of the data and students can personally experience exploring and analyzing the data with the graphing calculator which increases learning (Hollar & Norwood, 1999).
Using interactive technology, such as graphing calculators, in the mathematics classroom allows students to receive immediate feedback on the problems they are exploring. Immediate feedback often makes students feel excited and increases their interest in the topic being studied. When students are allowed to use interactive technology it gives them the opportunity to explore their own ideas and make their own discoveries through experience (Maestro-Scherer, Rich, Scherer, & Michell, 2002). As a result, the discoveries of students are more real and give them a better understanding of the concept being studied (Maestro-Scherer, Rich, Scherer, & Michell, 2002).
From a constructivist’s view point, graphing calculators are also very beneficial. They enable students to develop connections between concepts by providing many different representations (Reznichenko, 2007). Allowing students to experience concepts using the graphing calculator also has benefits. It was found that students, who were given the chance to have an experiential learning experience by using the graphing calculator, felt more comfortable with data in real-world situations than the traditional students who did not use graphing calculators (Hollar & Norwood, 1999). As well, allowing students to use graphing calculators does not affect the learning of traditional arithmetic and enables them to become better problem solvers (Hubbard, 1998). The use of graphing calculators in the learning process gives students a personal experience with analyzing data and gives them the opportunity to explore the effects of different values on functions and their graphs (Brown, 2004).
Graphing calculators also help struggling students develop better math skills by learning through experience with their graphing calculator. They use their graphing calculator as an aid for solving problems (Hubbard, 1998). The experience gained when using graphing calculators give students a better understanding of the relationship between equations and graphs, and using graphing calculators also encourages students to explore concepts (Caldwell, 1995).
Many students find it much easier to learn concepts in mathematics when they can see their findings as a graphical representation on the screen. Using the graphing calculator is also much easier and faster than figuring out on paper and then sketching. When students use this tool as an aid, they are experiencing the mathematical representations through the calculator which help them obtain a better understanding of the concept (Hubbard, 1998). Discoveries and connections made by students when using graphing calculators helps improve the student’s overall understanding (Hubbard, 1998). Graphing calculators also make it easy for students to access and see results, both computational and graphical. The use of graphing calculators in the classroom, during instruction, also increases computational skills and understanding of concepts, as well as enhances results on non-calculator tests. As a result, there has been an increased use of graphing calculators and other technology in mathematics classrooms (Reznichenko, 2007).
Atherton, J. (2009). Learning and teaching; Experiential learning [on-line]. Retrieved January 20, 2010 from http://www.learningandteaching.info/learning/experience.htm
Brown, J. (2004). A difficult function. Australian Mathematics Teacher, 60(2), 6 – 11.
Caldwell, F. W., Jr. (1995). Effect of graphing calculators on college students’ learning of mathematical functions and graphs. (ERIC Document Reproduction Service No. ED 393669)
Doerr, H. M. & Zangor, R. (2000). Creating meaning for and with the graphing calculator. Educational Studies in Mathematics, 41(2), 143 – 163.
Garofalo, J., Drier, H., Harper, S., Timmerman, M. A., & Shockey, T. (2000). Promoting appropriate uses of technology in mathematics teacher preparation. Contemporary Issues in Technology and Teacher Education, 1(1). Retrieved January 30, 2010 from http://www.citejournal.org/vol1/iss1/currentissues/mathematics/article1.htm
Goos, M., Galbraith, P., Renshaw, P., & Geiger, V. (2001). Promoting collaborative inquiry in technology enriched mathematics classrooms. (ERIC Document Reproduction Service No. ED 454055)
Graphing calculator. (n.d.) In Wikipedia, the free encyclopedia. Retrieved February 1, 2010 from http://en.wikipedia.org/wiki/Graphing_calculators
Harry, V. (2000). Technology advancing a continuous community of learners TACCOL): Integrating technology into teacher preparation. Making a Difference in the Learning of All Students. (ERIC Document Reproduction Service No. ED 440071)
Hollar, J C. & Norwood, Karen. (1999). The effects of a graphing approach intermediate algebra curriculum on students’ understanding of function. Journal for Research in Mathematics Education, 30(2), 220 – 226.
Hubbard, D. (1998). Improving student knowledge of the graphing calculator’s capabilities. (ERIC Document Reproduction Service No. ED 422175)
Hussain, Dr. I. and Adeeb, Dr. M. A. (2009). Role of mobile technology in promoting campus- wide learning environment. The Turkish Online Journal of Educational Technology, 8(3); 48 – 56.
Kolb, D. A., Boyatzis, R. E., & Mainemelis, C. (1999) Experiential learning theory: Previous research and new directions. Retrieved on January 29, 2010 from http://188.8.131.52/search?q=cache:upDlU9pP_gMJ:www.d.umn.edu/~kgilbert/educ5165- 31/Readings/experiential-learningtheory.pdf+Experiential+Learning+theory:+ previous+ research+and+new+directions.&cd=1&hl=en&ct=cl nk&gl=ca
Maestro-Scherer, J. B., Rich R. E., Scherer, C. W., & Michell-Nunn S. (2002). Technology in organizational learning: Using high tech for high touch. Educational Technology & Society, 5(2), 87 – 92.
Neill, J. (2006). Experiential learning & experiential education: Philosophy, theory, practice & resources. Wilderdom Outdoor Education. Retrieved on January 20, 2010 from http://wilderdom.com/experiential/
Reilly, M. (2009). Restoring points of potentiality: Sideshadowing in elementary classrooms. The Reading Teacher, 63(4), 298 – 306.
Reznichenko, N. (2007). Learning mathematics with graphing calculator: A study of students’ experiences. (ERIC Document Reproduction Service No. ED 497715)
Sabry, K. & Barker, J. (2009). Dynamic interactive learning systems. Innovations in Education and Teaching International, 46(2), 185 – 197.
Simundza, G. (1995) The fifth rule: Experimental mathematics. Retrieved on January 30, 2010 from www.oswego.edu/nsf-precalc/Simundza.doc
Smith, M. K. (2001). David A. Kolb on experiential learning. The Encyclopedia of Informal Education. Retrieved on January 21, 2010 from http://www.infed.org/biblio/b-explrn.htm