MTED 5318 - Meeting 2
MTED 5318 - Meeting 2 MTED 5318, Teaching and Learning with Techonology in the Mathematics Classroom
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This 6 page Class Notes was uploaded by Mitzelle Escobar on Sunday September 6, 2015. The Class Notes belongs to MTED 5318, Teaching and Learning with Techonology in the Mathematics Classroom at University of Texas at El Paso taught by Dr. David Carrejo in Fall 2015. Since its upload, it has received 16 views. For similar materials see Teaching and Learning with Techonologh in Education and Teacher Studies at University of Texas at El Paso.
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Date Created: 09/06/15
MTED 53 18 September 2 2015 Week 2 Working towards final projects Use the readings to help you Van Heile Reading are interesting geometry Continuation of last week s PP Mathematical Activity How much activity takes place away from the computer first have to answer what the emphasis is on for procedural or conceptual O The research is unclear about this issue 0 What are our thoughts I In the calls it will vary because it will depend on how some technology was developed I Example the calculator developed to work with teachers and students 0 As we look at the development of the TI calculator computer scientist and mathematicians get into the mix Therefore we engineers math people creating this tool it is purely scientific perspective for the use Now it is more difficult to incorporate into a classroom 0 Geogebra may not always be useful for some teachers because some of it is more scientific rather than pedagogical Despite different perspectives current research seems to have two perspectives in common 0 Activity using technology has to ENGAGE and REFLECT I Engaging Without it there is more of an uphill struggle to teach technology I Re ect Should allow students to deal with technology that is interactive the more interactive the better 0 Two Critical Questions I 1 Can technology afford us some ideas and techniques that are not normally possible through traditional means I Yes for example the use of infinity I 2 Can technology reinforce or perhaps worse create misconceptions 0 Sure due to limitations in the scientific realm that can happen 0 Ex Lines don t look connected due to the pixilation need to keep this in mind when using technology Mathematical Reasoning Three concerns form a mathematics perspective depends on perspectives of mathematics 0 Wanting to teach procedure or concepts what about both How do I make it meaningful to students I It is more of a challenge because it is the duty of teachers to find a way to join the two teaching types 0 1 tool use in mathematics I Symbols and symbolic manipulation O 2 Metacognition is it logical I Does my reasoning make sense I Use what you know so that you can relate back to the information you have given You will have to go into the truth for the re ective students who question what you teach or say 0 3 Abstraction and generalizability I Problem solving abilities we will call this modeling I Is related to asking if something makes sense I How to make students becoming better problem solvers a question a lot of researchers are still trying to solve I See logic in their reasoning I There is a procedure that is like a scientific method conducting a research 0 Researchers have found that students were given word problems were meant to reinforce a skill that was presented in the previous chapter 0 Later they tried to make the word problems more exciting rather than straight forward However there was no increase of understanding from students I A problem teachers face Curriculum Much research focuses on nontraditional curricula and nontraditional classroom settings Some research has altered the traditional curricula in significant ways e g the calculus reform movement Technology has pushed the concept of multiple representations in math education e g statistics functions and algebra 0 multiple representations not only represent the same problem but also the same idea I have something seen in two ways but still have the same problem I what is the difference between a fraction a decimal and a percent 0 All three the same but have different visuals I Also known as multiplicative reasoning 0 How do we represent a function I Expressed I Verbally I mapping graphing I computation y fX into a X t chart They all relate to relationships between numbersquantities If students see a dotted line we can later use it as a number line Video Comments Link found under Curriculum Food for thought The presenter Conrad Wolfram states that 0 To stop teaching calculating start teaching math 0 Use computers I Using computers in math is a silver bullet for making math education work Math is very popular just not in math education 0 Why teach math I 1 Technical jobs I 2 Everyday living 0 It is more quantitative than it used to be needed to make mortgage payments ect I 3 Logical thinking 0 Math is a way to teach logical thinking 0 What is math I 1 Posing the right questions I 2 Real world I math formulation I 3 Computation 4 Math formulation I real world verification Presenter states that students should only be doing number 1 2 and 4 That computers should be doing the computation 0 Rather than having students learn how to compute they should be learning other concepts while letting the calculator do all of the computations O Calculating is the machinery of math What do you not agree with 0 Where would we begin with what he was mentioning where is the cutoff point 0 He said that we do not need the basics but his classification of basics is different from what I would think it is 0 Geometry the first domain we will be covering Agenda Conceptual foundations of learning geometry how students construct the idea of arithmetic or patterns such as irrational numbers V2 0 The van Heile framework 0 Classification 0 Some basic constructions ruler and compass Technology introduction to GeoGebra 0 The teacher wants to go over it because we found out that there are going to be some problems we face when downloading it Abstract What is a good definition of abstraction form the constructivist perspective 0 Something that is not concrete or tangible You cannot touch it Only exist on paper It is too complicated too much thinking this concept really applies to geometry but is not related today Not something that strips away meaning seeing the likenesssimilarities in things that at first glance are not like each other Goes back to multiple representation it is about the relationships being the representations 0 It is not a pedagogy it is a way of learning OOOOOO Using Dynamic Geometry The idea of extractions all comes into play Concepts and Objects We refer to the early van Heile Levels to understand how students can rely on classification and categorization to form definitions in geometrv and develop spatial reasoning O E g students who do not classify or categorize will visualize or recognize objects that are approximately square but not truly square roots 0 However this begs us to ask an important question how round is your circle Within geometry we have certain ideas about what shapes look like and can be classified as O The teacher then drew a hand drawn circle and asked if it was a circle I Visually students would say yes I A mathematician engineer would say prove it I There are different definitions of what a circle is and what a circle should be I looks more at classification and categorization as mentioned above especially for geometry Diagrams The need to by physical tactile 0 The original definition of abstraction Representations run the risk of being objects consider the view from geometry The transition to the coordinate The Van Hiele Levels Level 0 visualization O Sorting and classifying shapes 2D and 3D 0 Constructing and dissecting shapes I Tangrams O Tessellation or tiling O Pentominoes a type of polyomino Level 1 analysis 0 Categories of 2D and 3D shapes I Sorting of properties sorting and classifying quadrilaterals which can branch out into similarities and congruency Level 2 informal deduction 0 Language of informal deduction I Words all some none ifthen what ifetc I Using a truefalse list 0 The Pythagorean theorem we will never rid of Pythagorean theorem good topic for the final I Informal proofs Level 3 deduction Level 4 rigor 0 Levels 3 and 4 high school aspect I Constructions I Logic I High school geometry proofs I For younger students the idea of a mathematical proof 0 they can use technology to try every possible thing to see if it changes such as trying to change the sum of the angles in a triangle on a computer until they finally say they cant Goes against Piaget because he is not categorizing the levels or breaking it down in depth 0 In terms of mathematical reasoning he looked at the concepts of geometry and foundations of calculus there were children that he was doing his interviews on but they would have all differed on level of Van Heile dealing with geometry and algebra GeoGebra Activity www2eoaebraorg Getting worldwide attention Gone over several innovations created by different teachers so that it could be used in the classroom Geogebra gt Create your own image Look at geometry 0 A big plane acting like a white sheet of paper 0 Provided with tools at the top 0 Has a lot of fundamental things 0 Can be used to show symmetry re ection translation dilation and rotation What was a fundamental thing that students will have to relearnrethink in a robust way in geometry Euclid s element because of constructions As we get into critical ideas we will see how this can be helpful in the classroom Download Geogebra on your computer we will be using it wwwgeogebraorgdownloads Also ipad to see the difference Work with it play with it o More conceptual ideas will be presented next week
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