MTED 5318 - Meeting 7 (October 7)
MTED 5318 - Meeting 7 (October 7) MTED 5318, Teaching and Learning with Techonology in the Mathematics Classroom
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This 5 page Class Notes was uploaded by Mitzelle Escobar on Wednesday October 7, 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 24 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: 10/07/15
MTED 5318 October 7 2015 Week 7 Review of last week Last week we reviewed modeling We will eventually be looking at calculus however I will not notify you that we are covering calculus O Show you how else they can apply the mathematics through technology but it will be fairly simple Homework 2 due 1014 Think about things differently but we will review the concepts that will be needed for the next homework today Second blackboard posting will be due the week after the homework 2 is due PowerPoint October 7 Geometry to Algebra FunctionB ases Reasoning Wants to start to put things together fully robust understanding of Function Ratio 0 Slope or rate of change 0 Becomes important when wanting to look at a curve to see the difference Patterns reasoning CoVariation teacher s belief of starting point for students 0 Exponential functions 0 Can make a connection to the information in a chart covariation through the ratio shown on the graph Multiple representations they are all intertwined and can go back and forth between these different concepts with uidity Question is where should students begin to learn functions A History of Algebra Babylonian in uence 0 No symbols spreadsheets Greek in uence 0 A connection to geometry and measure 0 Diophantus a move from geometry to syncopated algebra I This includes symbols such as letters ex 2x17 I Descartes thought xx was better than writing xquot2 I There was a huge debate about fxquot1 which secondary schools see as the inverse function of fx I Then came bout fxquot1 1fx which eventually was questioned as well Hindu amp Arabic in uence 0 Negative numbers and irrational numbers I Example of irrational number square root of 2 French in uence 0 Descartes amp Viete The Analytic Art symbols and geometry England in the 19th century 0 Abstract algebra I Example done in our class was symmetry I An algebra defined on a set of things Became most prominent in the early 19th century 0 Why What were the in uences I Academics I Vocational preparation Became less important prior to World War II 0 Why What were the issues I Algebra as modeling 0 Is algebra important now Why or why not I Yes the conceptidea of algebra is important because it represents a concept representation of patterns lhelps to develop logic I Food for thought from teacher what if I told you that there is actually a way to teach calculus without a lot of the technological machinery we are normally using in the traditional textbookclassroom Became very important again during the Cold War 0 Why What were the issues I Academics and the new math I engineering As far as looking at the history it becomes very complex in both arenas 0 Was not known as a simple thing in history 0 In school algebra there was very few of a difference about the complexity 0 More recently people are questioning if they should bring geometry back through functions and number based What does history tell us What are the con icts that we face today 0 The concept of variable and generally speaking the use of symbols the semantics The connections to geometry Fraction vs ratio reasoning The equal sign the concept of equivalence which was also huge Integers gt Complexity of it tells us who studies it and why OOOOO The Shifting Landscape of School Algebra Major challenges that are posed to us 0 Who studies algebra and why Algebra for all 0 When should we study algebra The case for early algebra I Most people say that we need to wait to teach students until they are mathematically mature enough for the concept 0 How is technology affecting us What role does it play in algebra Hs it become a new algebra Completing concepts of School Algebra Algebra as generalized arithmetic O Arithmetic s Addition subtraction multiplication and division Algebra as the study of functions 0 Example show 2Xl7 and 2Xly most people would think that they are two different things begin looking at this in 4th grade 0 We are starting to teach with 2X1y Algebra as language or a symbol system 0 Just follow the step by step procedures no understanding or comprehension of how or why something works 0 A lot of arguments saying that algebra should stay this way mathematics should be applied and have some meaning Early Algebra wwwtuftsedu Lesson materials tab provides different grade levels 0 Provides many lessons and they are free 0 Helps you to think outside the box on teaching algebra at the different grades Covariation and Modeling Students should develop a deeper understanding of the ways in which changes in quantities can be represented mathematically 0 If students can see something in covariation can they also see it in the graphs ratio 0 How we are looking at tables and graphs Even undergraduate students have difficulty modeling functional relationships 0 Again we need to see some uidity within tables and graphs To model dynamic events the concept of rate as a ratio is foundational Piaget s three stage theory 0 Construction of an image of change in some quantity 0 The coordination of images of two quantities O The formation of an image of simultaneous covariation of two quantities 0 all it means is that we are looking at graphs that students need to grasp Recall our work with tables O Covariation involves the coordination of variation in two or more columns as one moves up and down the table 0 Coordination between a table of values and the graph of the table involves the idea of a moving point being located somewhere on the graph and how it is traveling along the graph I A fundamental idea in calculus O Covariational reasoning therefore is defined as the set of cognitive activities involved in coordinating two varying quantities while attending to the ways in which they change in relation to each other including multiple representations Filling Water Bottles 1 Did you ever notice that when filling some bottles the water all of a sudden spurts out of the top Why does this happen a When pouring at a constant rate the volume decreases and the rate of change of the volume 2 Imagine filling each of the six bottles below pouring water in at a constant rate For each bottle choose the correct graph relating the height of the water to the volume of water that39s been poured in Sketch a Graph Sketch a graph for each of these situations No numbers or formulas are to be used The sketches for the responses are on the powerpoint the teacher posted I also listed them below as well 0 The temperature of a frozen dinner from 30 minutes before it is removed from the freezer until it is removed from the microwave and placed on the table Consider time 0 to be the moment the dinner is removed from the freezer I Time and temperature I Sketch 2 O The value of a 1970 Volkswagen Beetle from the time it was purchased to the present It is in top condition I Time and value I Sketch 4 O The level of water in the bathtub from the time you begin to fill it to the time it is completely empty after your bath I Time and level of water I Sketch 6 a bit more complicated because it indicates the points where people get into the bath tub 0 Profit in terms of number of items sold I Profit and items sold I Sketch 1 0 The height of a baseball in terms of time from when it is thrown straight up to the time it hits the ground I Time and height I Sketch 5 O The speed of the baseball in the situation in letter e I Time and velocity speed and direction I Sketch 3 Finishing notes We did not have time to completed get to the last activity that the teacher had planned 0 Nonetheless we will still be able to complete the homework with the two prior actiVities performed in class 0 We will cover it next week Remember that the homework is due next class period Also to keep up with the readings because we will be haVing a post after the homework