Blog#10: Recommendations for the Development of Future Mathematicians

As the math teacher, my daughter reaps the “benefits” of daily math facts flashcard practice. Although neither of us particularly looks forward to the drill and kill exercises, my experience of working with students in eighth grade who have not yet mastered basic computations reinforced the importance of such activities. Regardless of the level of enjoyment, it is absolutely critical to establish a strong foundation in basic mathematical skills in order to increase the likelihood of success in higher level math courses.

Bransford, Brown, and Cocking state that mastery and memorization are significant components of traditional education. However, research on development of expertise in a subject matter requires more than the recollection of facts. The child must have the opportunity to construct learning through inquiry-based instruction. Not only must teachers work to develop mathematical knowledge, but they must cultivate the students’ general problem solving skills.

I constantly look for everyday, hands-on activities that incorporate math skills. Simple actions such as working with my daughter in doubling a pancake batter recipe or keeping an accurate Yahtzee scorecard indirectly highlight the importance of performing mathematically-sound arithmetic operations. I find the integration of hands-on algebraic activities more difficult because algebra is infrequently used in everyday life experiences.

With the increase of technology and computer-based education however, relevant and engaging resources are becoming more widely available, although the quality of such tools is not guaranteed. Prior to using a program (web-based particularly), I ensure that the program is legitimate and worthy of the devotion of instructional time. To teach about slope and equations of linear and quadratic functions, I utilize a software program called Green Globs. I use Study Island, a web-based instructional tool aligned with state standards, to prepare students for PSSA testing. The Utah State University developed interactive algebra activities in its National Library of Virtual Manipulatives that are aligned with the National Council of Teachers of Mathematics Standards. This site includes activities that mimic classic games such as Peg Puzzle or Switch or Stick and the feedback is given immediately on the same screen.

Bransford, Brown, and Cocking advocate the practice of incorporating real-life problems and simulations into the classroom. In addition, they encourage opportunities in which learners receive feedback – whether it be from computer-based or directly from a teacher. These are just two of the numerous ways mentioned in “Conclusions and Recommendations for Research” chapter in which technology can assist with the establishment of effective learning environments.

As I continue to work to develop my algebra students’ mathematical abilities using a wide range of resources, I take great interest in assisting in the development of my daughter’s mathematical foundation by continuing the daily flashcard practice (against her wishes!) Although the world of virtual manipulatives, web-based tutorials, and Green Globs is remarkable, without a solid base in arithmetic operations, the activities are entirely ineffective.

References
Bransford, J.D., Brown, A. L., & Cocking, R.R., Eds. (1999). How people learn: Brain, mind, experience and school. Washington, D.C.: National Academy Press.