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EDU 365, teaching mathematics using technology notes weeks 1-7

by: amber karichner

EDU 365, teaching mathematics using technology notes weeks 1-7 EDU 365

Marketplace > Saint Joseph's University > Education > EDU 365 > EDU 365 teaching mathematics using technology notes weeks 1 7
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About this Document

these notes cover the material leading up to the final
Mathematics and Technology
Dr. Janine Firmender
Math, Technology, Teaching
75 ?




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This 7 page Bundle was uploaded by amber karichner on Tuesday September 13, 2016. The Bundle belongs to EDU 365 at Saint Joseph's University taught by Dr. Janine Firmender in Spring 2016. Since its upload, it has received 3 views. For similar materials see Mathematics and Technology in Education at Saint Joseph's University.


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Date Created: 09/13/16
9/8/15 Class notes Math and technology Technology principle  Technology is essential in teaching and learning mathematics; it influences the mathematics that is taught and enhances students’ learning. o Calculators, o TV/videos o Computers o Interactive white boards o Cellphones  How do we know what to teach in mathematics at each grade level? o Standards  Common core  State standards o Certain curriculum o School curriculum guide o Assessment information Behaviorism vs. Constructivism  Behaviorism o Positively reinforcement/punishment  Procedure/skill  Correct answers  Basic facts o Training specific response  Fixed order o Teacher-centered  Constructivism o Experimental  Constructing knowledge o Student centered o Teacher guided  Provide opportunities o Schema  Mental/concept map Class Notes 9/10/15 Math and technology  Recommendation #2 o Actively involve students  Exploration  Sense making  Metacognition  Communication  Recommendation #3 o Move to learning from concrete to abstract  Enactive stage (concrete)  Representing past events through appropriate motor response o “Touch a leaf” o “Move 5 blocks”  Learn by physical interaction with whatever the manipulatives are o Ex.: playing with building blocks  Iconic (semi-concrete)  Mental representation or picturing what is happening  Cannot physically move  Pictures/images o Ex.: using pictures of building blocks  Symbolic (abstract)  Use words  An abstract representation of something o Ex.: use the words “3 building blocks”  Recommendation #4 o Use communication to encourage understanding  Discussions with peers  Questioning  Welcome to ask questions  Orally or written communication  Talking about mistakes or the process o Teacher’s role in discourse  Prompt the conversation  Initiate/question  Guiding the conversation  Background knowledge Class notes 9/17/15 Math and Technology  Procedural knowledge o Skillful use of mathematical rules or algorithms o Ex. Lattice, standard, equations, etc.  Conceptual knowledge o Understanding meaning of mathematical concepts 9/24/15 Class Notes  What questions should we be asking ourselves when planning? o Assessment o Accommodations  ELL  IEP  High ability  Physical disabilities  Interests o Prior knowledge o Goals/objectives o Materials o Classroom setup o Location o Type of lesson  Intro  Review  Practice o Hook  Launch  Lesson plan analysis o How are the objectives stated?  Write additional, relevant objectives for the lesson  As a result of…  Concrete o A way to observe o Measure  Specific details  Do not use the words “know” or “understand” in the objectives 10/8/15 Class notes  Number sense o Understanding number concepts and operations o Strategies for handling numbers and operations o Compute accurately and efficiently, detect errors, and recognize results as reasonable o Use numbers understanding and strategies in flexible ways o Expectations that numbers are useful, meaningful and make sense o Life long process  Stages  Pre-number development  Early number development  Number development  Classification  Sorting according to characteristics/attributes  What is being counted  Attribute blocks  Venn-diagrams 10/20/15 Class notes  Counting principles o One to one rule  One to one correspondence o Stable order rule o Order irrelevance rule o Cardinality rule  Counting stages o Rote counters  Memorization o Rational counters 10/22/15 Class notes  Hindu-Arabic numeration system o Symbolic representation of numbers  Place value  Characteristics  Place value  Base ten o Once we get up to ten of something, we need to trade that in for the next highest ten base  Zero  Additive property  How do we develop place value? o Base ten blocks o Comparisons 10/29/15 Class notes  Computation o What does it mean?  Division  Calculating o Prerequisites for computation  Facility with counting  Possible but not efficient  Experience with concrete solutions  Familiarity with problem contexts  Experience talking and writing about mathematical ideas o How to develop meanings 11/3/15 Class Notes  Meanings for operations o Addition  Finding how many in all o Subtraction  Separation or take away  Comparison or finding the difference  Part-whole  Mathematical properties o Commutative property  5+7 is the same as 7+5  A+B=B+A  Thinking strategies for the basic facts o Addition  Commutative property  Adding one and zero  Adding doubles and near doubles  Counting on  Combinations to 10  Adding to 10 and beyond 11/19/15 Class Notes  Evaluating algorithms o Must have  Accuracy  Generality o Nice to have  Efficiency  Ease of accurate use  Transparency  Evalutate multiplication and division algorithms o Addition algorithm  Standard/traditional  Accurate o Yes  Generality o Yes  Efficiency o Yes  Ease of accurate use o Maybe  Transparency o No  Partial sums  Accurate o Yes  Generality o Yes  Efficiency o No  Ease of accurate use o Yes  Transparency o Yes


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