Month: March 2012

The vision of digital possibilities in mathematics creates further turbidity in the mathematics waters at this time. During this era of disagreement between teachers, between parents, between teachers and parents, and with the publication of and ensuing conversations from such articles as Maclean’s  “Why is it your job to teach your kid math?” (Reynolds, 2012), in British Columbia school districts are occasionally looking at and discussing technology in the elementary math classroom.  Realistically, most debate time is  spent on the topics of change in curriculum and pedagogy.

Theorizing about the teaching and learning of mathematics continues by researchers, educators, (Drijvers, Kieran, Mariotti, Ainley, Anderson, Chan, Dana-Picard, Guedet, Kidron, Leung, Meagher, 2010) and the public. Calls to my office from parents,  teacher meetings,  teacher learning sessions etc. are the work that most occupies me. There is little discussion in my world of technology in math.

I began teaching in in 1987 and was increasingly since that time the math instructional leader in my school. For the last decade I have held the district leadership position in numeracy. The late 1980’s through the 1990’s was an active time for theorizing in the teaching and learning of mathematics (Drijvers et al., 2010)  Hand held calculators, logo,  Plato, digital possibilities in the math class, were limited up to and through the end of the 1980’s. Calculators were part of my senior math years in the early 1970’s and in the late 1980’s and early 1990’s sporadically available in classrooms.

As the 1990’s progressed computers entered our homes and classrooms with greater frequency and students, teachers, and parents were introduced to digital math games.

Lucky was the teacher who had a computer in his or her classroom and a good supply of floppy discs.

Papert in his paper, Teaching children to be mathematicians vs teaching about mathematics, (1972), declares that teaching students about mathematics is not sufficient. Indeed students understanding mathematics is not enough. It is the doing of mathematics that is important. As a teacher of math, a district learning coordinator,  and a teacher of EDCP 340 Math Methods course, I can not agree more with Papert. It is the doing of math that enables students to construct understanding and to make sense of mathematical concepts. The 1980’s and 1990’s digital offerings taught students about math (perhaps), assessed to determine whether or not students understood concepts, but mostly had students practicing for speed skills which were previously learned. Yet there were those who envisioned more. Howson and Kahane, (1986), believed that schools would be under increasing pressure to “demonstrate that they were technologically aware” (p. 76). for an indirect glimpse at the kind of theories figuring in the discussions of the Study group participants.

Schools have been under increasing pressure yet the incorporation of technology into elementary math classes in our district has been slow. Document cameras and the occasional smartboard are in use. The myriad of digital numeracy activities that this cohort has been exposed to in ETEC 533 are not currently known to many in my district. When this course ends and the weekly posting, replying, and the assignments are done . . . then I suppose it will be my purpose to introduce and facilitate the use of digital math possibilities in classrooms.

Drijvers, P., Kieran, C., Mariotti, M-A., Ainley, J., Andresen, M., Chan, Y., Dana-Picard, T-D., Gueudet,G., Kidron, I., Leun, A., Meagher, M., & Leung, A. (2010). Integrating technology into mathematics education: Theoretical perspectives. In C. Hoyles & J-B LaGrange (Eds.) Mathematics Education and Technology-Rethinking the Terrain, 89-132.

Howson, A.G., & Kahane, J.-P.  (1986). School Mathematics in the 1990’s New York: Cambridge University Press.

Papert, S. (1972). Teaching children to be mathematicians versus teaching about mathematics, International Journal for Mathematical Education, Science, and Technology, 3, 249–262.

Reynolds, C. (2012, March 13). Why is it your job to teach your kid math?. Macleans, 135, 28-31.

I teach in a rural school district. I also teach teacher candidates who are specializing in rural education. For our students there are limited opportunities to visit museums, aquariums, theatres, and cultural events. We live in an area of British Columbia in which elk, osprey, and sturgeon are common wildlife but polar bear, emu, and ocean salmon are scarce. Our nearest volcano (Red Mountain) has been dormant for centuries. Only the occasional pleasure craft makes its way up or down the Columbia River. I chose to investigate Virtual Field Trips. Among the field trips that I embarked upon were virtual visits to the volcano fields of Costa Rica, the San Diego Zoo, and the Panama Canal.

The above sites held some interest for me. I read content, browsed media, and connected to links. My ten-year old son on the other hand responded to the San Diego Zoo visit with “I didn’t see anything. They (the elephants and polar bears) were either all sleeping somewhere else or maybe they died.” His lack of interest in the visit was because I had not given him purpose or facilitated reason for him to visit, discover, and investigate. The virtual field trips, like any resource, will be effective only if incorporated into learning activities well planned and supported by good practice. Good practice that is enhanced by collaboration and participation in a learning community.

A Virtual Learning Environment (VLE) may or may not have the four characteristics of a learning community as defined by Bielacyzc and Collins (1999). Valued members with expertise (scientists, teachers, enthusiasts, students) dedicated to learning and who support the sharing of knowledge and skills can work together.  The VLE’s that I visited were not stand-alone examples of learning communities. The virtual communities, for the most part,  that I linked to were places to visit and not yet developed as a places to live and learn deeply. There was one exception. Field Trip  Earth provided access to materials for emerging readers and strategies to assist. Field Trip Earth integrated subject areas purposefully. For example – literature circles were incorporated as well as activities for data analysis. Field Trip Earth gave a hint as to what could be.

The Exploratorium also offered more interactive possibilities and was engaging and could be incorporated easily as a learning resource.  Here again, to truly fit the definition of a learning community, Exploratorium would have to be well intentioned by the teacher.

The teacher is an essential element of any VLE. They must ensure  students are not overwhelmed and travelling only at the surface level of the experience, disengaged, or experiencing a loss of purpose. (Spicer and Stratford, 2001). Any Virtual Learning Environment should provide the opportunity for visual and audio stimulation. The teacher will still have to provide opportunities to provide somatosensory, olfaction, gustatory experience as is appropriate (although digital technology of the future may well affect these senses).

 

 

 

 

This past week’s assignment enabled me to collaborate with a colleague whose path I had crossed multiple times during our MET journeys. Both of us are near to the end of this learning adventure. The opportunity was greatly appreciated.  Just as it is for the learners in our classroom, the opportunity to work collaboratively resulted in a better product (lesson plan and discussion posting), and increased understanding of digital tools as resources. In that spirit of collaboration so too is this post created. – Denise Flick and Jasmine Virk

Srinivasan, Plamer, Brooks, and Fowler (2006) suggest, “To novices (students) . . . anything other than the real system is perceived as fake” (p. 140). My colleague and I questioned, how this finding might apply to the use of virtual manipulatives in the math and science classroom. Would learner attitude influence the effectiveness of digital manipulatives as tools? Should such tools be used sparingly, only in the absence of the real thing, or in combination with them?

Our fears were relieved as multiple sources provided evidence that increased engagement, motivation, and conceptual understanding can be achieved through the use of virtual math manipulatives (Crawford and Brown, (2003), Reimer and Moyer, (2005)).  Research supported the use of digital math manipulatives as a tool to provide an interactive environment with immediate feedback. Suh and Moyer-Packenham (2007), were persuasive in their views of using digital manipulatives to reduce the cognitive load for the learner allowing the learner to focus on the process and on constructing meaning.

It is critical that teachers choose technology based resources that facilitate beyond drill and practice and that can be employed in purposeful pedagogy and  in a constructivist learning process and that facilitate and enhance critical thinking and student centered learning. Such affordance to support meaningful learning  is not inherent in digital manipulatives. The selection of resources requires the professional judgment of the teacher digital or not.

Our own experiences in the classroom have confirmed for us the advantages listed by Burns (2001a as stated by Crawford and Brown, 2003).

•Manipulatives help make abstract ideas concrete.

•Manipulatives build learner confidence and enable them to easily test and confirm their reasoning.

•Manipulatives are useful tools for solving problems.

•Manipulatives make learning math interesting and enjoyable.

We developed an integrated math and science learning opportunity. A virtual manipulative resource was chosen. Simply titled, Virtual Manipulatve, the resource is intuitive, comprehensive, attractive, and easily adapted to a wide range of grade levels, strands, and concepts. Virtual representations of the commonly found “hands on” classroom manipulatives are included.The learning possibilities with this manipulative are endless. The primary purpose of the manipulative is to offer concrete visualization of mathematical concepts that will lead towards understanding of the mathematical concepts as defined by learning objectives.

A lesson was developed (Grade 3/Shape and Space/2D Shapes and 3D Objects) in which students were asked to sort objects using one or two attributes. Included in this activity are opportunities for students to:

•use Technology in a collaborative learning environment.
•Generate a demonstration of their understanding of 3D objects and their attributes.

•Evaluate their understanding in discussion and sharing with other students

•Modify their original mental models.
Students were then given the opportunity to locate and digitally record examples of 3D objects used in structures (Grade 3/Physical Science).

It cannot be assumed that all teachers include concrete math manipulatives when facilitating mathematical conceptual understanding. Virtual Manipulatives could be employed in student and teacher learning opportunities. As educational leaders within our districts, we see opportunities to use this resource with teachers to deepen mathematical understanding and enhance pedagogical practice. As teachers in classrooms where digital tools such as document cameras, smart boards, computers, notebooks, and personal devices are increasingly available this resource will be a valuable tool in daily practice.

Math:Science Grade 3 – 3D

References:

Crawford, C. & Brown, E. (2003). Integrating Internet-based Mathematical Manipulatives Within a Learning Environment. Journal of Computers in Mathematics and Science Teaching. 22(2), 169-180.

Reimer, K., & Moyer, P.S. (2005). Third-Graders Learn About Fractions Using Virtual Manipulatives: A Classroom Study. Journal of Computers in Mathematics and Science Teaching. 24(1), 5-25.

Srinivasan, S., Perez, L. C., Palmer,R., Brooks,D., Wilson,K., & Fowler. D. (2006).  Reality versus simulation. Journal of Science Education and Technology, 15 (2), 1-5.

Suh, J.,& Moyer-Packenham, P. (2007) The application of dual coding theory in multi-representational virtual mathematics enviroments. Retrieved March 9th, 2012 from http://www.emis.de/proceedings/PME31/4/208.pdf