{"id":290,"date":"2024-03-13T19:23:46","date_gmt":"2024-03-13T19:23:46","guid":{"rendered":"https:\/\/openlab.sps.cuny.edu\/knowledge-bank\/?page_id=290"},"modified":"2024-05-03T21:56:44","modified_gmt":"2024-05-03T21:56:44","slug":"general-problem-solving","status":"publish","type":"page","link":"https:\/\/openlab.sps.cuny.edu\/knowledge-bank\/general-problem-solving\/","title":{"rendered":"General problem solving"},"content":{"rendered":"\n
By Chandra Mongroo, Ph.D,<\/strong> Full-time Faculty and Doctoral Lecturer, General Education<\/pre>\n\n\n\n
This page offers diverse problem-solving approaches in mathematics, recognizing that different methods suit different situations or learning preferences. Having a range of strategies fosters flexibility, enriches understanding, and cultivates resilience, preparing individuals to tackle complex problems effectively across various contexts.<\/p>\n\n\n\n
<\/p>\n\n\n\n
A. Review of Problem Solving Process:<\/em> Polya\u2019s Problem Solving Techniques<\/a> (Berkeley Math)<\/h2>\n\n\n\n
Q: I read the math question but do not know where to start. How do I proceed?<\/em>

A: The key is to unlock the theme of the question. Here are some suggestions on how to begin: <\/em><\/p>\n\n\n\n
    \n
  1. Gather as much knowledge as possible from the problem. Highlight or underline key words. This is where you should return to the text and review the unit\u2019s vocabulary.<\/li>\n\n\n\n
  2. Re-visit worked out examples. Pay close attention to details in the problem solving process that are not clearly stated. Write out these steps with explanations in your notes. <\/li>\n\n\n\n
  3. Return to the question you were tasked with and approach it in a similar way as the text. <\/li>\n\n\n\n
  4. Analyze your solution. What did you solve? What does it mean in the context of the problem? Is it reasonable with the given constraints? <\/li>\n\n\n\n
  5. Report your results. Writing out a summary of your findings will help you reinforce the ideas that were developed in the problem solving process.<\/li>\n<\/ol>\n\n\n\n
    B. General Problem Solving Heuristics<\/em><\/h2>\n\n\n\n
    A heuristic<\/strong> is a general strategy for solving a problem. Here<\/a> you will find various examples of heuristics for problem solving (Ohio State University). <\/p>\n\n\n\n
    Worked Examples<\/a> (Lippman)<\/p>\n\n\n\n
    C. Estimating Solutions<\/em><\/h2>\n\n\n\n
    When problem solving, it is suggested to have an idea of your solution when you attempt a problem. Estimating solutions isolates concept application from numerical accuracy. Below are some useful videos. <\/p>\n\n\n\n
      \n
    1. Estimating Whole Number Sum & Differences<\/a><\/li>\n\n\n\n
    2. Estimating Decimal Addition<\/a><\/li>\n\n\n\n
    3. Estimating Decimal Differences<\/a><\/li>\n\n\n\n
    4. Estimating Whole Number Products<\/a><\/li>\n\n\n\n
    5. Estimating Decimal Products<\/a><\/li>\n<\/ol>\n\n\n\n
      You may find the term \u201csignificant digits\u201d, \u201csignificant figures\u201d, or \u201csig figs\u201d in a math or science related course. We say significant figures are specific digits in a number that are used to express precision.  <\/p>\n\n\n\n
      Useful resources:<\/strong><\/p>\n\n\n\n
        \n
      1. Practicing Sig Figs<\/a> (Purdue University)<\/li>\n\n\n\n
      2. A Short Guide to Sig Figs<\/a> (Yale University)<\/li>\n\n\n\n
      3. Worked Examples<\/a> (Libre Texts)<\/li>\n<\/ol>\n","protected":false},"excerpt":{"rendered":"
        By Chandra Mongroo, Ph.D, Full-time Faculty and Doctoral Lecturer, General Education This page offers diverse problem-solving approaches in mathematics, recognizing that different methods suit different situations or learning preferences. Having a range of strategies fosters flexibility, enriches understanding, and cultivates resilience, preparing individuals to tackle complex problems effectively across various contexts. A. Review of Problem […]<\/p>\n","protected":false},"author":63,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"portfolio_post_id":0,"portfolio_citation":"","portfolio_annotation":"","openlab_post_visibility":"","footnotes":""},"categories":[12],"tags":[],"class_list":["post-290","page","type-page","status-publish","hentry","category-math","post-preview"],"_links":{"self":[{"href":"https:\/\/openlab.sps.cuny.edu\/knowledge-bank\/wp-json\/wp\/v2\/pages\/290","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/openlab.sps.cuny.edu\/knowledge-bank\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/openlab.sps.cuny.edu\/knowledge-bank\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/openlab.sps.cuny.edu\/knowledge-bank\/wp-json\/wp\/v2\/users\/63"}],"replies":[{"embeddable":true,"href":"https:\/\/openlab.sps.cuny.edu\/knowledge-bank\/wp-json\/wp\/v2\/comments?post=290"}],"version-history":[{"count":8,"href":"https:\/\/openlab.sps.cuny.edu\/knowledge-bank\/wp-json\/wp\/v2\/pages\/290\/revisions"}],"predecessor-version":[{"id":463,"href":"https:\/\/openlab.sps.cuny.edu\/knowledge-bank\/wp-json\/wp\/v2\/pages\/290\/revisions\/463"}],"wp:attachment":[{"href":"https:\/\/openlab.sps.cuny.edu\/knowledge-bank\/wp-json\/wp\/v2\/media?parent=290"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/openlab.sps.cuny.edu\/knowledge-bank\/wp-json\/wp\/v2\/categories?post=290"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/openlab.sps.cuny.edu\/knowledge-bank\/wp-json\/wp\/v2\/tags?post=290"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}