← all pages
01:_Problem_Solving
view live ↗
<p class="lt-math-9827">Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. This chapter will help you develop these very important mathematical skills, so that you will be better prepared to help your future students develop them. Let’s start with solving a problem!</p> <p class="lt-math-9827"></p><div id="fac89a38-a99d-42de-bf6f-c64825a915c9" class="mt-guide-content"><div class="noindex"><ul class="mt-topic-hierarchy-listings mt-guide-listings"><li data-page-id="9821" class="mt-list-topics"><dl class="mt-listing-detailed"><dt class="mt-listing-detailed-title"><a title="1.1: Introduction to Problem Solving" class="internal" href="/https://math.libretexts.org/Bookshelves/Applied_Mathematics/Mathematics_for_Elementary_Teachers_(Manes)/01:_Problem_Solving/1.01:_Introduction_to_Problem_Solving"><span class="mt-icon-article-topic"></span>1.1: Introduction to Problem Solving</a></dt><dd class="mt-listing-detailed-overview"></dd></dl></li><li data-page-id="9822" class="mt-list-topics"><dl class="mt-listing-detailed"><dt class="mt-listing-detailed-title"><a title="1.2: Problem or Exercise?" class="internal" href="/https://math.libretexts.org/Bookshelves/Applied_Mathematics/Mathematics_for_Elementary_Teachers_(Manes)/01:_Problem_Solving/1.02:_Problem_or_Exercise"><span class="mt-icon-article-topic"></span>1.2: Problem or Exercise?</a></dt><dd class="mt-listing-detailed-overview"></dd></dl></li><li data-page-id="9823" class="mt-list-topics"><dl class="mt-listing-detailed"><dt class="mt-listing-detailed-title"><a title="1.3: Problem Solving Strategies" class="internal" href="/https://math.libretexts.org/Bookshelves/Applied_Mathematics/Mathematics_for_Elementary_Teachers_(Manes)/01:_Problem_Solving/1.03:_Problem_Solving_Strategies"><span class="mt-icon-article-topic"></span>1.3: Problem Solving Strategies</a></dt><dd class="mt-listing-detailed-overview"></dd></dl></li><li data-page-id="9824" class="mt-list-topics"><dl class="mt-listing-detailed"><dt class="mt-listing-detailed-title"><a title="1.4: Beware of Patterns!" class="internal" href="/https://math.libretexts.org/Bookshelves/Applied_Mathematics/Mathematics_for_Elementary_Teachers_(Manes)/01:_Problem_Solving/1.04:_Beware_of_Patterns"><span class="mt-icon-article-topic"></span>1.4: Beware of Patterns!</a></dt><dd class="mt-listing-detailed-overview"></dd></dl></li><li data-page-id="9825" class="mt-list-topics"><dl class="mt-listing-detailed"><dt class="mt-listing-detailed-title"><a title="1.5: Problem Bank" class="internal" href="/https://math.libretexts.org/Bookshelves/Applied_Mathematics/Mathematics_for_Elementary_Teachers_(Manes)/01:_Problem_Solving/1.05:_Problem_Bank"><span class="mt-icon-article-topic"></span>1.5: Problem Bank</a></dt><dd class="mt-listing-detailed-overview"></dd></dl></li><li data-page-id="9826" class="mt-list-topics"><dl class="mt-listing-detailed"><dt class="mt-listing-detailed-title"><a title="1.6: Careful Use of Language in Mathematics" class="internal" href="/https://math.libretexts.org/Bookshelves/Applied_Mathematics/Mathematics_for_Elementary_Teachers_(Manes)/01:_Problem_Solving/1.06:_Careful_Use_of_Language_in_Mathematics"><span class="mt-icon-article-topic"></span>1.6: Careful Use of Language in Mathematics</a></dt><dd class="mt-listing-detailed-overview"></dd></dl></li><li data-page-id="10154" class="mt-list-topics"><dl class="mt-listing-detailed"><dt class="mt-listing-detailed-title"><a title="1.7: Explaining Your Work" class="internal" href="/https://math.libretexts.org/Bookshelves/Applied_Mathematics/Mathematics_for_Elementary_Teachers_(Manes)/01:_Problem_Solving/1.07:_Explaining_Your_Work"><span class="mt-icon-article-topic"></span>1.7: Explaining Your Work</a></dt><dd class="mt-listing-detailed-overview"></dd></dl></li><li data-page-id="10156" class="mt-list-topics"><dl class="mt-listing-detailed"><dt class="mt-listing-detailed-title"><a title="1.8: The Last Step" class="internal" href="/https://math.libretexts.org/Bookshelves/Applied_Mathematics/Mathematics_for_Elementary_Teachers_(Manes)/01:_Problem_Solving/1.08:_The_Last_Step"><span class="mt-icon-article-topic"></span>1.8: The Last Step</a></dt><dd class="mt-listing-detailed-overview"></dd></dl></li></ul></div></div><script type="application/json" id="mt-localizations-guide-tabs-settings">/*<![CDATA[*/{"MindTouch.IDF3.label.guide.settings.classifications":"Classification settings","MindTouch.IDF3.label.guide.settings.learningpath":"Path settings","MindTouch.IDF3.label.overview.max.count":"{0} characters remaining.","MindTouch.IDF3.label.overview.max.count.over":"Warning. {0} characters will be truncated.","MindTouch.LearningPath.dialog.remove.cancel":"Cancel","MindTouch.LearningPath.dialog.remove.confirm":"OK","MindTouch.LearningPath.dialog.remove.header":"Remove path","MindTouch.LearningPath.dialog.remove.message":"You are about to remove this path from this guide."}/*]]>*/</script>
💾 Save to sandbox
Reset