Mathematics

Promoting students' skills in mathematics through use of ICTs

Catherine Peddle, Memorial University of Newfoundland

This position paper argues in favor of the need to integrate information technology into the teaching and learning of face to face mathematics into the classroom. In the traditional classroom the teacher lectures, utilizes the chalkboard and provides seatwork to present mathematical concepts. How effective is this? Today teachers have the opportunity to promote students’ skills in mathematics with the integration of technology into his or her mathematics lesson. Students of today are born into a world of technology that is part of their daily routine. Utilizing this technology in the classroom should enhance their mathematical skills.

Problem

Teaching mathematics in face to face learning in a traditional classroom poses challenges for the teacher to develop students’ mathematical skills. The following studies address specific problems with teaching mathematics face to face. According to Ross, MaDougal, and Hogoboam-Gray (2002) there is evidence that traditional mathematic programs taught using face to face instruction leads to mastery of basic algorithms without conceptual understanding.

Traditional approaches to teaching mathematics are not facilitating productive classroom discourse that allows students to develop habits of mind to engage with mathematics (Walshaw, 2008).

According to McLoghhlin (2013) to increase learner engagement with mathematical problem solving the development of instructional model with flexible and learner centered experiences is needed. Traditional teaching is not enhancing active engagement of students’ mathematical concepts because students need to learn complex concepts in a flexible, self paced manner ( McLoghlin, 2013).

Pianfetti’s (2000) findings were similar to McLoghlin’s (2013). According to Pianfetti’s (2000) study students in the traditional face to face teaching classroom tend to perceive mathematics from a textbook perspective , which means students have difficulty transferring what they learn in class to events they may encounter in their daily lives ( Pianfetti, 2000 ). Students have difficulties understanding concepts such as distance over and then applying them to concrete events(Pianfetti, 2000 ).Thus, instruction needs to involve new ways to help students better understand abstract concepts (Pianfetti,2000 ).

Pianfetti’s(2000) study can be linked to Main and O’Rourke’s ( 2011) study in Australia. According to Main and O’Rourke (2011) The Review Panel of National Numeracy in Australia in 2008 showed concerns over poor numeracy skills in students. Students were not being engaged in the traditional face to face math instruction resulting in lack of fluency in basic math facts and a limited development of higher order mathematical skills( Main and O’Rourke, 2011).There was a need for a more engaging delivery of the curriculum and a collaboration to enhance mathematical understanding ( Main and O’Rourke, 2011).

Role of ICTs

The problem can be addressed through Information Communication Technology (ICT). ICT can promote students learning of mathematical concepts. The following studies address solutions.

Edwards, Rule, and Bloody (2013) studied two mixed ability classes, one class using online laptop learning and the second class receiving traditional face to face learning for ten different math topics. Achievement results were similar for both classes (Edwards, Rule, & Bloody, 2013). Edwards, Rule, and Bloody (2013) recommend blending both modes of learning, online learning and face to face instruction together for best student achievement. A specific finding for the benefit of using online learning with face to face instruction was that students who have difficulty attending to or comprehending the language of a typical lecture, benefit from web based tools (Edwards, Rule, & Bloody, 2013).

In a study of first graders, differences were examined that exist among academic achievement of those students who were learning using virtual manipulatives and those who were taught with the traditional text and practice activities (Brooks,2006). According to Brooks (2006), the use of virtual manipulatives as an instructional tool was more effective than traditional text activities. Students received immediate feedback (Brooks, 2006).

According to Wright (2010) it is clear that information technology tools support learning mathematics from feedback from ICT learners. One of the key findings on computer instruction was that when the student is in control over his or her learning than the effects were greater than when the teacher was in the control (Wright, 2010).

According to Luterbach (2013) elegant instruction goes past traditional instruction because it is effective, efficient and inspiring. Examples in Luterbachs’ study focus on the benefits of applications of information communication technologies and mathematics which give learner a knowledge and a sense for the real world applicability of a concept (Luterbach, 2013). The next study addresses the teacher’s point of view of using ICT. Glazer (2004) followed a teacher who previously taught with limited technology in mathematics, completed a course with Intermath materials and later integrated technology enhanced mathematical investigations in her classroom. According to Glazer (2004) the teacher commented, “I have become very proud. Its not what I’m doing, but what they’re (the students) doing there. I have been much more observant of different types of peer interactions and learning. That’s been much more rewarding for me than seeing tests to grade (p.5).” An innovative learning solution is mobile learning, which involves handheld technologies to improve teaching and learning (Kalloo and Mohan, 2012) .A mobile learning application offered the learner multiple strategies for learning mathematics such as game based learning( Kalloo and Mohan,2012).

The final four studies reflect results specific to teaching and learning geometry. According to Santos (2008) students developed problem solving skills,as a result of, using Cabri Geometry software. A result of this study was that students using software were engaged in a line of reflection in which their teachers allowed them opportunity to visualize, explore and connect diverse mathematical contents and problem solving (Santos, 2008). Starcic (2013) found that, “Computer didactic programs, allow students, a more natural passage through the first three levels of geometric reasoning( problem visualization, problem analysis, and forecasting solutions) than the paper-pen tasks usually required of students (p. 5).”

According to Kang (2011) traditional education in mathematics has focused on facts rather than applications while increased intensity of graphic information in computer-generated instruction can hold students’ attention and information in mind. Virtual intense images were helpful with advanced geometry problems (Kang 2011). Garcia (2007) studied a debate on the use of computers versus pencils for the study of descriptive geometry. The results showed the combination of laptop computer and projector was the preferred method of instruction because computers have been able to improve the technical branches of drawing (Garcia, 2007).

Obstacles

There are obstacles to promoting mathematical skills with information communication technology.

According to Glazer (2004) technology training for teachers can fall short when needed to enhance student’s learning. In Glazer’s (2004) study a teacher successfully learned to use technology tools in a workshop and received support to use this technology to enhance her students’ learning. With a cognitive apprenticeship model she received support until she could independently implement technology enhanced mathematical investigations (Glazer, 2004).

According to Bos (2009) virtual manipulatives can be difficult to maneuver and cause a student frustration. However, when students are given detailed instructions, examples and guidance to use these virtual manipulatives abstract concepts will become more concrete and the students will gain a higher conceptual understanding (Bos, 2009).

According to Wright (2010) networked handheld technologies are used to run small software owned by someone who is not part of the classroom, the software programmer. The teacher may find it difficult to help in learning unless requested by the student (Wright, 2010). As well, the software may be too challenging or easy (Wright, 2010).To prevent this obstacle from happening the teacher and learner need to use the handheld technologies as problem solving tools and with joint understanding, thus the teacher has to become familiar with the technology before using it in his or her classroom (Wright, 2010). Wright (2010) identified another obstacle which would be learners in an individual experience. However, teachers can promote social interaction using technology such as providing mathematical activities where students submit their solutions to a public display, iniating justifications of solutions (Wright, 2010).

According to Garcia (2007) some people believe that computers cannot substitute a pencil in a student’s hand since they do not have the versatility or availability in technical drawing. However, programs such as Macromedia Flash facilitate geometry and visualization systems (Garcia, 2007). Computers have brought an evolution to the technical branches of drawing Garcia, 2007).

Works cited

Bos, B.(2009). Technology with cognitive and mathematical Fidelity: what it means for the math classroom. Computers in the Schools, 26(2), 107-114. Url: http://dx.doi.org/10.1080/07380560902906088

Bouck, E., & Gauri, J. (2012). Assistive technology and mathematics education: reports from the field. Journal of Computers in Mathematics and Science Teaching, 31(2), 115-138

Edwards, C., Rule., & Bloody, R. (2013). Comparison of face to face and online mathematics learning of sixth graders. Journal of Computers in Mathematics and Science Teaching, 32(1), 25-47

Garcia, R., Quiros, J., Santos, R., Gonzalez, S., & Fernanz, S.(2007). Interactive multimedia animation with Macromedia flashes in descriptive geometry teaching. Computers & Education, 49(3), 615-639.

Glazer, E. (2004). From a caterpillar to a butterfly: the growth of a teacher in developing technology – enhanced mathematical investigations. Journal of Technology and Teacher Education, 12(1), 114-138.

Hu, X., & Craig, S. (2012). The effects of a traditional and technology- based after school program on 6th grade students mathematics skills. Journal of Computers in Mathematics and Science Teaching, 31(1), 17-38.

Hwang, W., & Hu, S. (2013). Analysis of peer learning behaviors using multiple representations in virtual reality and their impacts on geometry problem solving. Computers & Education, 62, 308 -319.

Hollebrands, K. (2007). The role of a dynamic software program for geometry in the strategies high school mathematics students employ. Journal for Research in Mathematics Education, 38(2), 164-192. http://www.jstor.org/stable/30034955

Kang, H. & Zentall, S. (2011). Computer-generated geometry instruction: a preliminary study. Educational Technology Research and Development, 59(6), 783-797.

Luterbach, K. (2012-2013). Elegant instruction. Journal of Educational Technology Systems, Vol. 41(2), 183-204. Doi: http://dx.doi.org/10.2190/ET.41.2.f

Main, S. & O’Rourke, J. (2011) New directions for traditional lesson: can handheld game consoles enhance mental mathematical skills. Australian Journal of Teacher Education, 26(2), 43-55.

McLoughlin,C. (2013). Scaffolding conceptual learning in mathematics technology enhanced pedagology, a preliminary evaluation of student engagement with screencasts. AACE Journal, 20(1), 259-265.

Pianfetti, E. (2000). From the abstract to the practical: how motion media grapher helps students understand and interpret mathematical concepts. AACE Journal, 20(1), 328-333.

Ross, J., & McDougal, D., & Hogoboam-Gray, A. (2002). Research on reform in mathematics education. Alberta Journal of Educational research, 48(2), 122-138.

Santos, T., & Cristobal, E. (2008). Emerging high school students’ problem solving trajectories on the use of dynamic software. The Journal of Computers in Mathematics and Science Teaching, 27(3), 325-340. http://search.proquest.com/docview/220641623?accountid=12378

Starcic, A. I., Cotic, M. and Zajc, M. (2013), Design-based research on the use of a tangible user interface for geometry teaching in an inclusive classroom. British Journal of Educational Technology, 44: 729–744. doi: 10.1111/j.1467-8535.2012.01341.x

Steen,K., Brooks, D., & Lyon, T. (2006). The impact of virtual manipulatives on first grade geometry instruction and learning. The Journal of Computers in Mathematics and Science Teaching ,25(4), 373-391. http://search.proquest.com/docview/220637236?accountid=12378

Vani, K., & Permanend, M. (2012) Correlating questionaire data with actual usage in a mobile learning study for high school mathematics. Electronic Journal of E Learning, 10(1), 76-89. http://search.proquest.com.qe2a-proxy.mun.ca/docview/1010336132?accountid=12378

Walshaw, M., & Anthony, G.(2008). The Teacher’s role in classroom discourse: a review of recent research into mathematics classrooms. Review of Educational Research, 78(3), 516-551. http://www.jstor.org/stable/40071136

Wright,D.,(2010). Orchestrating the instruments: integrating the ICT in the secondary mathematics classroom through handheld technology networks. Technology, Pedagogy and Education, 19(2),277-284. http//dx.doi.org/10.1080/1475939x.2010.491239.