Paying a tithe (10% of earnings)

In Sunday School, I teach kids who are turning 7 this year. There is a lesson manual and a schedule to follow, but I like bringing in authentic tasks (especially when it is math-related!) whenever possible.

Today the lesson was “I can pay tithing.” We talked about the meaning of tithe (Merriam-Webster says: “to pay or give a tenth part of especially for the support of the church”).

I brought a sack of pennies (about one-year’s accumulation!) and gave each of the kids a pile. I asked them, “Find out how many pennies you have and then tell me how many pennies you’ll give for tithing.”

Multiple Answers

One child said, “I’ll give them all.” I responded, “Sure. You don’t have to give all of your pennies, but you can. Do you still want to?”  “Uh-huh.” “Why do you want to give all of them instead of just 10%?” “Well. I don’t need them. I could keep some.” After church was finished, he came running back to tell me “I kept some of my pennies but I put some on the ground so that someone can find it for a lucky penny!”

Another child said, “I’ll give 4 because I’ve got 43 pennies.” I responded, “Okay. How did you figure that out?” “It’s easy! Every time I count 10 pennies, I take one.”

Another child said, “Can I keep the extra pennies?” I responded, “Sure!” “Okay, I’ll give 17 because I have 39 pennies.” “Okay, how did you decide to give 17?” “Because it looks like half.” “Ok. You can decide how much you want to give. The church asks for 10% but it’s okay to give more. Do you still want to give 17?” “Uh-huh!”

I gave them each a tithing envelope, they filled out their own slip (mostly), put the pennies in the envelope, and brought them to the bishop.

Assumptions

Sometimes in textbooks a word problem is given and the question asks: “Which should you choose?” or “What’s the best choice for Rohit?” Those problems make me cringe because it is making an assumption that “optimization” means the same thing for everyone, especially when some context is given. In this example, the kids all have different reasons for wanting to keep or give away the pennies – some told me they have $20 or $30 at home to spend, so maybe they don’t value pennies much. Others were already making plans for how they would spend their pennies. Some kids are just too darn nice.

But, if I pushed them to only pay 10%, then it feels like I’m making an assumption that you should always give the minimum. At the same time, by not pushing them to pay only 10%, I feel like I’m telling them they should always pay more than the minimum. So, even for me, I’m not sure what the “right” response is in this real-world math problem.

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Preparing to Write a Research Proposal

When I was working on my Depth paper for Comps, one of my committee members asked if I had filled out questions similar to the following to guide my thinking as I prepared to engage in research.

Judy Olson’s Ten Questions

From: CEP901a Educational Psychology Prosem; Judy Olson’s Ten Questions

Use the questions to write a proposal or paper, plan a research project, think about your future, or check up on your progress.

  1. What is the problem? (in the theoretical debate, the world)
  2. Who cares? (an argument about its importance)
  3. What have others done? (the lit review, but pointed as an argument)
  4. What is your approach? (your general approach, the new idea)
  5. What are you going to do explicitly? (your operationalization, investigation)
  6. What will happen? (or did happen, if you have results)
  7. What does this mean? (in terms of answering the problem)
  8. Who cares? (in what way is this important?)
  9. Where will you publish these results?
  10. What will you be doing in 5 years?

Judy Olson was Professor in the department of Psychology and the School of Information, and Director of CREW (the Center for Research on Electronic Work) at the University of Michigan. She has since moved to UCIrvine. She used these questions in a seminar for doctoral students in the School of Information (SI) during several terms in the late nineties. I [Raven McCrory?] was a doctoral student at the time (in education, contemplating a joint degree with SI) and was privileged to be in her seminars.

Dissertation Sketch

The following summer (2014) I was working on developing my dissertation proposal. It seemed to me that people often say that the process of writing a proposal is linear (i.e., figure out the problem, come up with a research question, then find a method that will answer the research question). But that seems (to me) to be an over-simplification of my process, anyway. My process of developing my dissertation research study was a cyclic, iterative process of getting to know what it was that I really cared about, how I could make it interesting / critical for other people, and how I could find answers to my questions in a way that worked for the question and for me.

So, I would work on the research question, think about the participants I could include, think about the literature I was reading and problems I saw referenced in that literature, etc.

Therefore – I tried to start out with a very lightweight summary of my interests, so I could use that as a way to focus conversations as I talked with my advisor and committee members. So I created this simplification that I called a “dissertation sketch” (see below for an example “sketch”).

  • What is the problem?
  • What is your purpose (briefly)?
  • What is your research question(s)?
  • Research Design
    • Give an overall picture of your plan.
    • What kind of data will you collect?
    • Who are your participants?

Example Sketch (keep in mind that these are very informal)

  • Sketch 1
    • What is the problem?
      • Both MET1 & METII recommend teachers develop a framework of technology choice and use.
    • What is your purpose (briefly)?
      • Develop a framework or a set of questions teachers could ask themselves as they look for tech or turn to fitting it into lessons.
    • What is your research question(s)?
      • Roughly: How can teachers intentionally develop their tech/math/teaching muscles? That is, how to develop a framework of tech choice and use?
    • Research Design
      • Give an overall picture of your plan.
        • Work with teachers on developing their frameworks, starting with a general framework. Ralph and I have done this to some extent in CEP 805, so that could give me a first step to working with other teachers. I could use the course now and next spring as one step of my project and then working one on one with teachers in their practice as a second step? Or could I contact our former students to ask about their interest in participation in such a study?
        • What we have done in the 805 is:
          • select literature that (hopefully) focuses teachers attention on types of learning and some characteristics that are important in integrating technology use;
          • asking teachers to answer several questions about tech tools they choose from a menu we provide;
          • giving more freedom in choice (teachers search and choose tech tools)  adding more questions to answer: asking teachers to search for tech tools and answer a larger set of questions
      • What kind of data will you collect?
        • Field notes / artefacts / video of development
      • Who are your participants?
        • Practicing teachers enrolled in CEP 805 and then
        • Practicing teachers in Michigan
        • Pilot phase:
          • students’ work from Spring 2014 CEP805 (not-publishable);
          • develop plan for Phase 1
        • Phase 1:
          • get IRB for permission next spring to more formally do this;
          • develop PD module from results
        • Phase 2:
          • implement PD module in phase with MI practicing teachers
  • Sketch 5
    • What is the problem? (in the theoretical debate, the world)
      • Both MET1 & METII recommend teachers (and PSTs) develop a framework of technology choice and use?
    • What is your purpose (briefly)?
      • Build a framework based on “best practices” for searching/implementing tech in math lessons based on practicing teachers who are (or consider themselves or are considered) tech experts.
    • What is your research question(s)?
      • How do “expert” teacher tech users choose and use tech?
    • Research Design
      • Give an overall picture of your plan.
        • Ethnography type observation of teachers who self-identify as tech gurus — how they choose it: strategy for searching and planning; how they use it: classroom norms, discourse, student activity & evidence (would hope to find variety in these characteristics)
        • Compare how these teachers use technology – are there important differences in their strategies or type of use?
      • What kind of data will you collect?
        • Getting a picture: Initial survey to identify  possible participants and to get an overall view of teachers’ self-identification of themselves as tech users
        • Field notes + screen capture/camera recording of teacher searching & planning; possible debrief after choosing a tech but before implementation
        • Field notes + video of implementation
    • Who are your participants?
      • Mathematics teachers who self-identify as tech gurus