The LEAP Curriculum Integration Model and Mathematics Problem Processing

Curriculum integration can appear as such a distant abstract concept. In fact, it is intensely personal to the lives of children and older learners as well.

Though problem processing really begins in the messy but interesting world around us, the first Look stage of problem identification and posing has been routinely left out of the mathematical curriculum of my three sons over the last 13 plus years of their education. Tests, worksheets and classroom experiences in math have exclusively started with a page of problems to be solved. The emphasis has not been on the relevance of mathematics, but on learning to work the systems of solutions discovered by those with mathematical sense. Though much discussion is given to the step of observation in science class, in reality, little authentic work with real unsolved problem areas is provided. Math and science too often provide students with almost no sense that there is a place for them to make their mark with their own contributions until well into coursework that comes years after they have had to make important career directing decisions. It is little wonder over the last twenty years that there has been a steady and significant decline in the number of college graduates seeking careers in math, science, business and information technology, areas which generally require at least one higher level mathematics course in calculus. This decline continues in spite of the strong need for and consequently higher salaries for such graduates in order to support and expand our high technology culture. Note below the different terminology for the same stages of problem solving.

Integrating Math-Science Curriculum Language and Technology for Problem Processing
Curriculum Focus
Technology Focus
. Math Science Local Actions

(e.g., calculators, spreadsheets, databases,  word processing, outlining, draw, paint, video, audio, animation, virtual reality, )

Global Tools
(networks of computers)
  • Identify problem and understand it
  • Problem Posing
  • observe
  • find, read, cut, copy, paste, renumber, outline 

    (humans, not computers, choose problems and purposes)

    Search online databases ; know online contact & reference systems; data space transport protocols
  • Propose strategies, such as: 
    • Guess and check (if multiple choices) 
    • Make an organized list (if logic problems) 
    • Look for patterns (if repetition problems) 
    • Draw a diagram (if word problems) 
    • Act it out (if collaborating) 
    • Work backwards (if long problems) 
    • Do a simpler related problem (if haven't seen the problem before)
  • analyze merits
  • choose strategies or strategy
  • Problem Solving
  • develop hypotheses 
  • conduct experiments 
  • draw conclusions
  • type, record

    (humans, not tools, generate and elaborate)

    computer conferencing (Netnews, LISTSERVs), collaborative screen use of any program, collaborative writing, talk, chat, email, GIS (Graphic Information Systems)
  • Execute strategy.
  • Check the problem and the correctness of the answer.
  • Persuasion check, lookup, read, listen 

    (tools have nothing to say about the substance of the teacher and learner's work)

    email, groupware, netphone, video conferencing (CU-SeeMe, private networks)
    Publish/ Perform
  • share findings
  • share findings
  • table of contents, index, format, print 

    (humans, not tools, have value systems thru which to appreciate or take comparative measurement of the works of others)

    Net tools: FTP; audio and video streaming; World Wide Web; virtual reality; wireless palmtops & PDAs.
    Legacy systems: TV, radio stations, publishing houses.
    Expanded Curriculum Integration Table (10 columns)

    The language invoked by science and math deserves to be more strongly integrated across their content areas. Note in particular the terminology at the Evoke stage, expressions that each support the goals of the other.

    Chapter Parent Frame | Updated March 6, 2004 | Page author: Houghton