Engaging students: Compound interest

In my capstone class for future secondary math teachers, I ask my students to come up with ideas for engaging their students with different topics in the secondary mathematics curriculum. In other words, the point of the assignment was not to devise a full-blown lesson plan on this topic. Instead, I asked my students to think about three different ways of getting their students interested in the topic in the first place.

I plan to share some of the best of these ideas on this blog (after asking my students’ permission, of course).

This student submission comes from my former student Andy Nabors. His topic, from Precalculus: compound interest.

What interesting (i.e., uncontrived) word problems using this topic can your students do now?

I would give the students a problem to find out where they should invest their money. They would be given several options with pros and cons and need to choose the best option for them and explain their reasoning. The problem would go something like this:

You are looking to put your graduation money, a total of $2,498, into a savings account. You have gone to several banks and found the interest rates and start-up fees for making an account there. Which bank is offering you the best deal? Which would you choose and why?

Bank	Interest Rate	Compounded	Start-Up Fee
Bank of America	2.5%	daily	$65
CitiBank	5%	monthly	$100
Comerica	3%	weekly	$50
JP Morgan	1.7%	continuously	$50
Wells Fargo	3.3%	bi-annually	$0

This material is Pre-Cal, so I assume the students are either juniors or seniors, so they may be looking at having to open a bank account of their own in their near future. Then this would be a relevant question for them to look into and figure out what exactly gives them the best option.

How could you as a teacher create an activity or project that involves your topic?

This activity would be similar to one we did in 4050. At the time of this activity, they would not know the formula for compound interest. I would put the students in pairs and pose the question “Suppose you have $1000 that earns 8% interest. How much would you have at the end of 2 years if the interest was compounded: a.)annually b.) biannually c.)quarterly d.)daily”. Then the students would work in pairs to figure out the answers and I would instruct the students to find a pattern as they worked to make it easier. The students would eventually discover the formula for compound interest compounded for any number. They would then be asked how many times the money would have to be compounded to put out the highest total. The students would discover that the higher number, the more total, but as the compounded numbers increased, the difference between the outputs would decrease. So we could then say that there is a limit to how much the output could be, and that limit would be compounded infinitely. Then we could take the limit and find out what the formula is for finding compound interest compounded continuously.

How can technology be used to effectively engage students with this topic?

Students need to know how to do their own research in their future for things like buying a house or car, choosing whether or not to rent or buy, or other things where they are having to find the best deal and fit for them. This activity would have students researching different banks. They would be asked to find out the details on certain banks’ interest rates. They would need to find out about fees and how many times the interest is compounded. They would need information about at least three banks, and then would need to research on independent sites which bank would be the best to start an account with from the banks they chose. Then they would choose a bank for them based on their own findings and calculations, and would choose a bank based on what an online article said. This would let students form their own opinions based on data they found, and weigh that data against the opinions of others. Their findings and opinions may not match up, and that’s why this activity would benefit them. It’s important that students learn to not take the opinions of others as fact, but do their own research to find the best deal.

Collaborative Mathematics: Challenge 12

I’m a few months late with this, but my colleague Jason Ermer at Collaborative Mathematics has published Challenge 12 on his website: http://www.collaborativemathematics.org/

A defense of the Common Core

I read the following defense of the pedagogical strategies behind the Common Core: http://www.vox.com/2014/4/20/5625086/the-common-core-makes-simple-math-more-complicated-heres-why

I really have no issue with the article itself. Sadly, the article does not address the two great deficiencies in the implementation of the Common Core: (1) homework problems and other assessments to gauge the depth of a student’s conceptual understanding of mathematics in ways that are age-appropriate, and (2) the direct tying of high-stakes tests based on the Common Core standards to the assessment of teachers.

I don’t feel like replicating my previous posts on this topic, so I’ll refer to my past posts here: https://meangreenmath.wordpress.com/2014/12/18/common-core-subtraction-and-the-open-number-line-index/

Scenes from the “Real World” where math is useful

This made me laugh: http://mathwithbaddrawings.com/2014/10/08/scenes-from-the-real-world-where-math-is-useful/

Gender Stereotypes in STEM

From the article Gender Stereotypes in STEM:

The study, which compared white and black women’s participation in and perception of STEM fields, found that black women were more likely than white women to show an interest in studying STEM disciplines when they enter college.

The research also shows that African Americans were less likely than white Americans to view STEM programs as masculine, which may help explain why the participation levels vary between the two ethnic groups.

The authors argue that race and ethnicity influence the gender stereotypes that women hold, which in turn influence their interest in the sciences, said Laurie O’Brien, an associate professor of psychology at Tulane University and one of the article’s lead authors.

Despite the findings of higher initial interest reflected in the journal article, other data show black women are underrepresented in the number of STEM bachelor’s degrees actually earned, according to the paper.

Helping Mathematics Students Survive the Post-Calculus Transition

Every so often, I’ll publicize through this blog an interesting article that I’ve found in the mathematics or mathematics education literature that can be freely distributed to the general public. Today, I’d like to highlight Michael J. Cullinane (2011) Helping Mathematics Students Survive the Post-Calculus Transition, PRIMUS: Problems, Resources, and Issues in Mathematics Undergraduate Studies, 21:8, 669-684, DOI:10.1080/10511971003692830

Here’s the abstract:

Many mathematics students have difficulty making the transition from procedurally oriented courses such as calculus to the more conceptually oriented courses in which they subsequently enroll. What are some of the key “stumbling blocks” for students as they attempt to make this transition? How do differences in faculty expectations for students and student expectations for themselves contribute to the “transition dilemma?” What might faculty incorporate into students’ learning experiences during the transition to help students better navigate the shift from procedural to conceptual, from concrete to abstract? This article offers some lessons learned in connection with these questions.

The full article can be found here: http://dx.doi.org/10.1080/10511971003692830