{"title":"Fitting a Line to Data","authors":"","doi":"10.1090/text/002/08","DOIUrl":"https://doi.org/10.1090/text/002/08","url":null,"abstract":"4 Learning involves what psychologists call dissonance: Unless people see that they don't understand, they can't really learn. Learning an idea involves adjusting your concepts so that the new idea fits. Because we want our students to understand, we might rush to explain concepts rather than let students come to realize on their own that they don't understand. Try to decrease your student's frustration with not understanding a concept right away. Show how your own curiosity allows you to welcome initial questions and confusion as an opportunity to learn.","PeriodicalId":220550,"journal":{"name":"Elementary Mathematical Models","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-08-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129696167","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Exponential Functions","authors":"Michelle Northshield","doi":"10.1090/text/002/10","DOIUrl":"https://doi.org/10.1090/text/002/10","url":null,"abstract":"The exponential function is probably the most recognizable graph to many nonmathematicians. The typical graph of an exponential growth model shows that the values have a slow initial growth leading to a rapid increase in value. The simple doubling function 2, 4, 8, 16, 32... is probably the simplest case of an exponential but they can be used to model many situations: describing growth in populations, money investments, spread of disease and decay of radioactive substances or depreciation of value. Over the past few years, I have noticed that my students can recognize graphs and tables that model exponential growth and decay when contrasted with a linear model, but lack the understanding of the algebraic properties of the exponential functions. By discussing the basic concept of function, followed by a look at the algebraic structure of the exponential function, this unit will represent a different approach. We will examine the set of exponential functions and discuss their algebraic properties. By developing this unit, I hope to develop a student population with a sense of understanding for the equation of the exponential function. I will be presenting this unit to a first year algebra class.","PeriodicalId":220550,"journal":{"name":"Elementary Mathematical Models","volume":"315 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-08-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121336679","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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