Introduction
The scope of this study is to assess the impact of using web-based resources in the teaching of mathematics on students’ attitude and learning.
Three factors define the scope of this study:
- To determine if visual representation of mathematical concepts and interactivity enhances learning
- Impact on student attitude and motivation
- To determine feasibility of using of tools that are freely available from the perspective that limited financial resources should not constrain teachers from use of computers in classroom teaching.
8 students of Grade VIII and 7 students of Grade VII at an international school in Bangalore, India were a part of this study. Given the qualitative nature of the study, the small sample size enabled interaction and discussion at depth.
Student profile
Most students had access to computers at home and used it mostly to play games, watch videos and search for information on school projects. Only a few of them used computers for accessing educational websites/ CDs or doing homework assignments. Their past academic performance varied significantly, indicating that the student representation was not homogeneous.
Current practice
The school chosen for the study is a new school, only in its second year of operation. The school has a computer lab with internet access but it was not yet used in teaching any subject. It served more as a resource center for staff and also for students to create their project reports.
The regular mathematics teachers are aware that web-based resources can be used in teaching. However, practical difficulties in structuring lessons and lack of awareness of specific resources that suit the curriculum limit them from actually incorporating web and other computer based resources in teaching of mathematics.
Strategy
The first step was to identify freely available web-based resources relevant to the school curriculum and due to be covered in the first semester of the current academic year (2009-10).
The next step was to teach the students the selected topics over a 3-day period. The motivation levels and attitudes were assessed through observation, feedback collected in writing at the end of every class and finally a group discussion. Learning was assessed through a short pen and paper test covering the topics that were taught using the web-based resources.
Identifying the web-based resources
The web-based resources were identified through internet search and from educational resources such as MERLOT (Multimedia Educational Resource for Learning and Online Teaching). The topics covered (sources listed in Appendix 1):
Grade VIII
· Introduction to quadrilaterals
· Nets
· Linear equations in 1 and 2 variables
· Time- distance & velocity
Grade VII
· Fractions
· Linear equations in one variable
The resources were identified keeping in mind the following criteria:
· Provide an opportunity for interactivity
· Show dynamically the impact of manipulation
· Allow students to investigate without the fear of going wrong
· Did not require any training for use
Research process
The sessions were conducted in the computer laboratory and it was possible to alternate between using a whiteboard and the computers.
A text file containing links to the web-based resources was copied onto each computer. Students were first introduced to the topic using a regular whiteboard and then a brief instruction was given to the students on how to use the web resource.
Given the limited number of computers available, most students had to share them, with one computer to two students.
As this was the first time the computers were being used, it was decided that the scores of the test would not count towards their annual assessment. Feedback was collected in writing at the end of each day. The group discussions were conducted on the third day, after the test.
Assessment of Learning
Grade VIII
Time-distance:
The relationship between time, distance and speed was understood by most students. However, only the academically stronger students managed to produce a correct graph using the information provided in the question.
Linear equations:
While students understood that a linear equation in two variables represents a straight line, identifying points on the line by x and y coordinates and the concept of slope seemed to be difficult. This was their first exposure to the coordinate geometry and the students clearly needed more preparation before introduction of (and more time with) the web based resources.
Quadrilaterals:
During the computer lab session, the students were able to independently identify relationships between the sides and the angles and summarize the properties of various quadrilaterals by manipulating the figures in the web-based resource. However, in the test, they struggled when they were expected to determine the measure of an angle or length of a side in a trapezium.
Nets:
In a quiz conducted just after this session, most students were able to match a polyhedron and the corresponding net. However, in the final test conducted on the third day, the students did not fare as well as anticipated. Students could identify a pyramid but encountered difficulty in identifying a tetrahedron. More students had success with a simple application of Euler’s formula.
Grade VII
Fractions:
As there was some prior exposure to this topic, it helped students in understanding the concepts. Most students were able to answer the related questions in the test.
Linear equations in one variable:
Students did not appreciate the analogy of a balance. While this was not investigated at depth, it is attributed to a great extent to students carrying out mathematical operations mechanically, without trying to understand the reason why a certain term was added to or subtracted from both sides of an equation. Observations, Feedback & Discussion
Access to a computer is fairly easy with most students already having a computer at home. All students were quite familiar with the use of the computer and relevant software.
Student feedback
Grade VIII
“The websites were fun and creative as we ourselves could solve our doubts. Before I found all these shapes to be complicated and boring, but these seem to be very easy now “Student A
“I liked the opening and closing up of the nets and playing with the figures” Student B
“We could really see the object and play around with it…This has been one of the most interesting class I had even though I do not like maths” Student C
“It was good but quite confusing” Student B
“I haven’t understood everything yet but I liked the software a lot” Student C
Grade VII
“We learnt something completely unknown to us and I found it very interesting” Student D
“At first I didn’t understand how to do the algebra but when I understood about it I felt very happy” Student E
“The class was interesting but I did not understand algebraic expression” Student F
The motivation levels were high and there was substantial participation in the class across both the grades. All the students enjoyed learning mathematics using the web based resources. They enjoyed self discovery by manipulation of sliders, interaction with figures representing fractions, quadrilaterals, nets and straight lines. The feedback at the end of everyday indicated that the students clearly enjoyed the sessions and found them interesting. They wanted their future lessons to incorporate the web-based resources. Students were eager to note down the links so that they could practice at home as well.
About half the students felt they now liked learning mathematics more. Some students were keen that the software provides them with feedback when a particular input/ action is wrong. These observations are consistent with those reported elsewhere (Hannafin, Burruss and Little, 2001).
Students reported difficulty in understanding linear equations, evident from the quotes above.
Student pairing
Student pairing does seem to have a powerful role to play. In pairs with students of differing abilities, the weaker ones also demonstrated increased interest and participation. In pairs, where both the students were academically strong, they explored the resources provided to a greater extent and asked more questions. Weak students were not paired together.
The students expressed a need to record on paper what was learnt using the computer as the on- screen manipulations are not accessible in preparation for a written test.
To summarize the differences observed between students, they have been grouped into: “Strong” and “Challenged” based on their past performance in examinations and meaningful classroom participation. These are not meant to reflect their intelligence or any other such measure. “Strong” implies better academic performance and constructive participation in the classroom while “Challenged” implies relatively weaker academic performance.
Strong students | Challenged students |
High motivation levels through all sessions and desire to use computers more in their learning | High motivation levels initially but lost interest if unable to cope, leading to seeking distractions- clicking on irrelevant icons, changing screen magnifications, going to other sites etc. |
High interest levels in mathematics continue to hold | Significantly increased interest expressed in learning mathematics |
Seek independence requesting that the computer program prompt them if a suggested solution is wrong | Expressed need for guidance, simpler visual representation and more preparation in terms of raising the level of prior knowledge. |
Prior mathematical techniques used sometimes posed a challenge. e.g. mechanically transferring terms from left hand side to the right hand side by changing the sign in a balanced equation as against adding/ subtracting the same term from both sides | In simplifying a balanced equation (to find the value of a variable), identifying which term needs to be added/ subtracted was not easy |
Had used the computer as a tool for learning and doing school projects. | Comfortable in using a computer but had never used it as a tool for learning |
Concerns such as those expressed by prospective teachers in Hazzan (2002/2003) become evident. Representing mathematical ideas on a computer did help visualization and stimulate thinking but inadequate preparation on manipulation of algebraic expressions posed difficulties.
Conclusion
- Visual representation and interactivity does enhance student learning and motivation.
- It is possible that the stronger students may gain more in the short term. Given the high motivation levels, over a longer period of time, it is anticipated to be beneficial to all the students. To ensure that this happens, student pairing needs to have a strategic approach. The suggested approach is to group together students of different abilities and shuffle partners periodically, monitoring the groups to ensure that they remain cohesive.
- It is possible to use freely available/ inexpensive web based resources and applications for the teaching of mathematics. However, a limitation of using these freely available resources is that it is not be possible to have a consistent pedagogical approach and on- screen environment, given that sources would be different.
- An instructivist learning environment as advocated by Hannafin et al. (2001) would work well: Accommodating learners’ needs and prior knowledge but limiting the amount of content available. Wherever possible, the on-screen information should be limited to what is needed for a student at a particular level- if fractions to be taught are limited to denominator less than 20, the teacher must have the option to restrict the application accordingly.
- Worksheets need to be devised based on the activities done using the computer so that students have a record for revision and can also share it with parents at home.
- The activities need to well planned and integrated into the classroom routines. Introduction to the topic, preparing students for what to expect is important before the computers are switched on. Students must be asked to switch the monitors off when their attention needs to be diverted to the whiteboard.
- Given that the students in Grade VIII and VII consistently expressed their discomfort with Algebra, it would be advisable to adopt an embodied approach with visualization as recommended by Tall (2009), to ensure that students are comfortable with Algebra at higher levels.
Appendix: List of resources used
Grade VII
Lesson 1: Linear equations
http://nlvm.usu.edu/en/nav/frames_asid_324_g_3_t_2.html?open=instructions&hidepanel=true&from=vlibrary.html
Lesson 2: Fractions
http://nlvm.usu.edu/en/nav/frames_asid_102_g_1_t_1.html?from=topic_t_1.html
http://illuminations.nctm.org/ActivityDetail.aspx?ID=45
http://nlvm.usu.edu/en/nav/frames_asid_159_g_2_t_1.html
Grade VIII
Lesson 1a: Quadrilaterals
Lesson 1b: Nets
Lesson 2: Linear Equations
http://www.waldomaths.com/Linear2NLW.jsp
http://www.bbc.co.uk/schools/gcsebitesize/maths/algebra/graphsact.shtml
Lesson 3: TIME DISTANCE
http://mathdemos.gcsu.edu/mathdemos/jogger/jogger.html
Hannafin, R. D., Burruss, J. D., & Little, C. (2001). Learning With Dynamic Geometry Programs: Perspectives of Teachers and Learners. The Journal of Educational Research, 94(3), 132-144.
Hazzan, O. (2002/2003). Prospective High School Mathematics Teachers’ Attitudes toward Integrating Computers in Their Future Teaching. Journal of Research on Technology in Education, 35(2), 213-225.
Tall, D. (2003). Using Technology to Support an Embodied Approach to Learning Concepts in Mathematics. In L. M. Carvalho & L. C. Guimarães (Eds.), História e Tecnologia no Ensino da Matemática (Vol. 1, pp. 1-28). Rio de Janeiro, Brasil. Retrieved 31-Aug-2009 from http://www.warwick.ac.uk/staff/David.Tall/pdfs/dot2003a-rio-plenary.pdf
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