Problem Solving Based Instruction and Its Shortfalls (Everyday Mathematics)

         There is an urgency in our educational policy to prepare students better to compete in the global economy. The Trends in International Mathematics and Science Study of 2009 showed the US students ranking 11th in Science and 9th in Math, with many Asian and Eastern European counterparts ahead of them. The new educational reform had stressed the need to teach and incorporate problem solving into curriculum, especially when it comes to mathematics and science.

             The problem solving based instruction, also known as, inquiry and/or discovery learning, holds that students learn best when given an opportunity to construct their own knowledge in an unguided or minimally guided environment. Furthermore, in addition to having students construct their own knowledge, inquiry based learning assumes that students acquire knowledge solely through experience.

                 Problem based learning approach was introduced in the health science program at McMaster University in Hamilton, Ontario (Canada), fifty years ago. Today, most medical programs and many undergraduate and graduate programs utilize some form of problem based learning throughout the United States. The medical students are supposed to be skilled at problem solving and have background knowledge of the content in order to successfully participate in the problem based learning, as noted by the McMaster University website (chemeng.mcmaster.ca/pbl/PBL.HTM).

              In 1985, the University of Chicago Department of Education introduced Everyday Mathematics, which is problem based learning math curriculum for elementary school students. Presently, Everyday Mathematics is widely implemented throughout Florida and the rest of the nation. The program is currently being used in over 185,000 classrooms by almost 3,000,000 students (everydaymath.uchicago.edu). The What Works Clearinghouse at the U.S. Department of Education (2010) found the program to be “potentially positive”, however, there needs to be a more thorough study conducted before the program can be declared effective. Presently, there is no single large scale study conducted on effectiveness of the program on students achievement in mathematics despite the nationwide program implementation and support by federal education funding.

                   Everyday Mathematics curriculum rests on constructivist theory of learning though inquiry and problem solving. After all, problem solving is a current staple goal of national mathematics and science curriculum. Unlike traditional mathematics curriculum, Everyday Mathematics does not teach algorithm and it does not promote drill of mathematical foundations in any form, such as, multiplication tables, addition, and subtraction. The amount of curriculum topics are numerous and are presented in non-sequential order. On any given day, a student in third grade can work on a wide range of unrelated math problems, from finding parameter of a rectangle to telling time.

                   In Everyday Mathematics children are encouraged to connect their prior knowledge of mathematics to the problem at hand. During their inquiry into the problem solving, students are supposed to create their own algorithm to the mathematics problems in order to show that they “get” the learning material. The Everyday Mathematics program is learner centered and students receive minimal or no guidance at all during their problem solving.

              Critics of Everyday Mathematics have pointed out that the programs constructivist nature is effective with a certain type of learner, such as, gifted and expert/university students. When novice elementary students are required to make their own algorithm without having sufficient mathematical foundation on which to base their problem solving, their working memory, which can only manage two to three new elements become overwhelmed and their learning suffers. In addition, without sufficient schema to process new information, students are likely to have false starts that further lead to misconceptions and failed learning (Moreno, 2004). Research found the knowledge of context and background knowledge to be the key elements of successful problem solving.

                 In order to engage in an effective and successful problem-solving activity, students need to work within familiar and realistic contexts that use familiar background schemas and prior mathematical foundations. Only then will students be able to transfer their learning to other problems and contexts (DeBono, 1983; Kirkley, 2003). On the other hand, when students learn science through unguided discovery with no or minimal feedback, they experience cognitive overload and are likely to form false start and misconceptions (Brown & Campione, 1994; Sweller, 2004).

                  The lack of background and/or context knowledge and minimal guidance are major obstacles in students ability to create their own algorithm and problem solve, especially when it comes to developing problem solving skills, which could then transferred to new problems. Kirschner, Sweller, & Clark (2006) found that the minimally guided instructional approach goes against over half a century of research on human  cognitive architecture and overwhelming evidence that minimally guided instruction is both less efficient and less effective.

                Consequently, it can be concluded that the premise and practice of the Everyday Mathematics is inconsistent with the current research of human cognition, as well as, in contradicting accepted working and long term memory theories. Research indicated that students need explicit instruction of novel information and when instructional guidance is absent cognition and new-old knowledge integration fails (Kirschner et al, 2006; Aulls, 2002).

               If we expect our students to compete in the global economy, we need to provide their schools with curriculum that aligns with learning and educational theories. It is simply not enough to believe that any curriculum is “successful” without prior large-scale extensive independent research.

                                            References

               Aulls, M. W. (2002). The contributions of co-occurring forms of classroom discourse and academic activities to curriculum events and instruction. Journal of Educational Psychology, 94, 520–538.

               Brown, A. L., & Campione, J. C. (1994). Guided discovery in a community of learners. In K. McGilly (Ed.), Classroom lessons: Integrating cognitive theory and classroom practice (pp. 229-272). Cambridge, MA: MIT Press.

               DeBono, E. (1983). The direct teaching of thinking as a skill. Phi Delta Kappan, 64, 703-708.

               Kirkeley, Jamie (2003). Principles For Teaching Problem Solving. Retrieved on (February, 2011). www. plataeam/down loads/papers/paper_04. pdf, 2003 – Citeseer.

              Kirschner, Sweller, & Clark (2006). Why Minimal Guidance During Instruction Does Not Work: An Analysis of the Failure of Constructivist Discovery, Problem- Based, Experiential, and Inquiry-Based Teaching. Educational Psychologist, 41,(2), 75-86.

               McMaster University. Problem-Based Learning, Especially In the Context of Large Classes. Retrieved from http://chemeng.mcmaster.ca/pbl/PBL.HTM.

               Moreno, R. (2004). Decreasing Cognitive Lead for Novice Students: Effects of Explanatory versus Corrective Feedback in Discovery-Based Multimedia. Instructional Science, 32,(1), 99-113.

              National Center For Education Statistics (2011).Trends In International Mathematics and Science Study. Retrieved from http://nces.ed.gov/timss/

              Sweller, J. (2004). Instructional design consequences of an analogy between evolution by natural selection and human cognitive architecture. Instructional Science, 32, 9–31.

               The University of Chicago School Mathematics Project Everyday Mathematics (2011). Curriculum Features. Retrieved from http://everydaymath.uchicago.edu/about/curriculum.

                What Works Clearinghouse (2010). Intervention:Everyday Mathematics. Retrieved from http://ies.ed.gov/ncee/wwc/reports/elementary_math/eday_math/index.asp

Lena M. Ed

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2 thoughts on “Problem Solving Based Instruction and Its Shortfalls (Everyday Mathematics)

  1. BTW, I think that Everyday Math sucks too. It’s inconsistent and confusing.
    It’s not “constructivist” at all. It’s a series of poorly conceived worksheets in
    random order.

    Scott Foresman tested “new math” on my 4th grade class in 1960-61 in San Jose, CA . We had stapled typed textbooks. Our teacher, a teacher in training from the university, and two professor-types from the corporation were in our classroom to test the efficacy of the program. I loved it. I was doing my babysitter’s algebra
    homework.But obviously the real world application had a different outcome.

    It’s very important to develop from the grassroots up, not from the phds/corporations down. Teachers need number sense — a personal understanding of what numbers are and how they work. Math is not about memorization. It’s about seeing patterns, relationships, and processes quickly and facile-y (is there such a word?) It requires an experience of how to think and reason in a particular way.

    Great experiences? Start with CandyLand and work through Yahtzee and cribbage. Shop with a small allowance (without help). Count by 3s, 4s, 6s, etc. Add/subtract lists of numbers in their heads in the car.

    Forget the corporate programs and play.

  2. LR above wrote: “It’s very important to develop from the grassroots up, not from the phds/corporations down.

    Sadly the US Gov. and the major forces playing this game have a disdain for actual valid research. Take the extremely flawed “Exemplary and Promising” math programs pushed by US Secretary of Education Richard Riley in 1999, which included Everyday Math …. no research just philosophical alignment with what the powers that be would like to have work.

    Read Hattie’s Visible Learning…. this is from my review at Amazon ==>

    —-
    [effect sizes from “Visible Learning” by Hattie : the hinge effect value of 0.40 or greater indicates an intervention is likely to bring success]

    Seattle’s current math direction is centered on:
    a. Inquiry based teaching (0.31)
    b. Problem based learning (0.15)
    c. Differentiated Instruction (no empirical evidence)

    Consider the effective practices Seattle chooses not to use:
    a. Direct Instruction (0.59).
    b. Problem Solving teaching (0.61),
    c. Mastery Learning (0.58), and
    d. Worked Examples (0.57).

    These four innovations are not only effective but could be easily combined into a deliverable package. Instead Seattle chooses to buy expensive to deliver programs that do not work.

    Seattle blunders on and your school and district is likely to do the same.
    Medicine went from an immature profession to one based on evidence because the clients demanded it.
    These days the immature profession of education appears headed to being an infantile profession. Only with lots of pressure will it become a mature profession.
    ——-

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