The definition of a “math person”

It has been awhile since I have posted here. My new responsibilities as the math department chair have taken up quite a bit of my time – but I am certainly relishing the opportunity to put into practice many of the ideas I have espoused here on GodandMath over the years. One of my responsibilities has been hosting a series of math talks for parents. This has been a great way for me to meet more families in our school community and to have a platform to explain our department’s philosophy of math education. This post is a summary of that philosophy that I have been sharing with parents.

Our department’s number one aim is to cultivate the mathematical affections of students – a phrase I have written about numerous times here. Essentially, the aim is to provide students a meaningful experience of mathematics that solidifies their appreciation of the discipline regardless of their future studies or career trajectories. This goal is in contrast to the prevailing attitude of society towards their mathematics education, summed up in the phrase “I’m not a math person.”

I start these parent meetings by asking who in the audience has ever said or thought “I’m not a math person”? I then ask for a few brave volunteers to explain what they mean by that. Without fail (whether in these parents meetings or in any context when someone admits to me that they aren’t a math person – which always seems to happen whenever you tell someone you’re a math teacher) there explanation falls somewhere along the lines of: I couldn’t remember all the rules, I wasn’t good at memorizing multiples, I never completed the problems fast enough, etc. Basically reiterating the prevailing view of society that to be a math person is to be efficient and accurate in computation and factual recall.

My typical response to people is “Yeah, I hate that stuff too. But I’m still a math person. What you’re describing isn’t how I see math. Can I show you how I see math?”

Our goal is to give students a very different impression of mathematics than what society has. We want to take away from students this go-to opt-out phrase of “Well, I’m not getting it, I’m just not a math person.” Mathematics, true mathematics, is inviting and uplifting for everyone.

How we as a department aim to cultivate students’ mathematical affections is through developing problem solvers. Below is a working summary of how our department defines problem solving (written to the student).

Defining Problem Solving: [1]

 Problem solving has been defined as what to do when you don’t know what to do. In some of your math classes, you probably learned about mathematical ideas by first working on an example and then practicing with an exercise. An exercise asks you to repeat a method you learned from a similar example. A problem is usually more complex than an exercise, so it is harder to solve because you don’t have a preconceived notion about how to solve it.

Problem Solving Expectations:

  1. Perseverance: Humility paired with confidence. Grit. In this class you will be asked to solve some tough problems. You will be able to solve most of them by being persistent and by talking with other students. When you come across an especially difficult problem, don’t give up. You may find that sometimes your first approach to a problem doesn’t work. When this happens, don’t be afraid to abandon the approach and try something else. Be persistent. If you get frustrated with a problem, put it aside and come back to it later. But don’t give up on the problem.
  2. Collaboration: You will be expected to talk to your classmates! Your teacher will ask you to get help from one another.
  3. Communication: In addition to working with your classmates, reading the book, and learning from your teacher, you will also be expected to communicate about your work and your mathematical thinking. You will do this by presenting your solutions to the entire class and by writing up complete solutions to problems. You will do presentations and write-ups, because talking and writing allow you to show your thinking. These communication processes will further develop your thinking skills.
  4. Grace: When you work with other students, you are free to make conjectures, ask questions, make mistakes, and express your ideas and opinions. You don’t have to worry about being criticized for your thoughts or your wrong answers.
  5. Service: Your growth in your math educational journey is not just about you. If the big problems of this world (curing disease, ending hunger, ending human trafficking, addressing sustainability, etc.) are going to be solved then mathematics will play a central role in their solution. If you are going to truly become a problem-solver then there has to be action taken.

At this point, after having explain our departmental goals and philosophy, I return to my original question.

“Ok, so you may not be a math person. But do you believe in the value of perseverance? Do you think collaborating in community and communicating ideas well are important skills? Do you believe in showing others grace and receiving grace yourself? I should hope so in our Christian community. Do you believe that we are called to serve others and put their needs before our own? If you said ‘yes’ to any of these, then congratulations, you’re a math person!

 

[1] Adapted from Johnson, K. & Herr, T. Problem Solving Strategies: Crossing the River with Dogs and Other Mathematical Adventures, 2nd Ed., Key Curriculum Press, 2001.

 

Advertisements

The Dance of Number


danceOfNumberCover

James Nickel, author of Mathematics: Is God Silent?, has completed his mathematics curriculum The Dance of Number and it is now available for order.

From the author’s website:

The Dance of Number is a sequenced and tightly integrated curriculum involving four textbooks totaling 1924 pages (Grades 7-10). The only prerequisite is above average reading comprehension. We start from ground zero, teach the basics of arithmetic from a fresh, vibrant perspective, and then take the reader on a journey that leads to the borderlands of the mountain range called Calculus. There are plenty of side roads along the way where we stop to gaze at the scenic beauty (i.e., a unified look at principles of Algebra, Geometry, Trigonometry). It is a long trip; its completion is worth the effort.

The texts are not named Algebra I or Algebra II, etc., because the four-volume sequence tells an coordinated story engaging the student in the nature of the structure of number, the development of its history, and its interpenetration with science. As the student takes this journey, all the topics of Arithmetic, high school Algebra, most of Geometry, and a complete study of Trigonometry are unfolded.

Because of this harmonized approach, these texts are different than most of what is on the market. The author wants the student to see how the ideas/branches of mathematics interpenetrate (e.g., you are doing algebraic operations and geometrical procedures as you are learning the elements of trigonometry). Our current textbook structure is not that successful at doing this.

After this sequence is completed, the student would be ready either for a complete course in Geometry (if desired) or PreCalculus

The series is published through Amazon’s Createspace. The author page is here.

Here is my favorite review, from Dr. Mark Eckel, one of the first ever guest contributors to GodandMath.

Work of a lifetime. People are known for their contributions in fields of inquiry, participation in great events, experiments which create discoveries, and ideas which break down walls of unknowing. Few are they whose life work assists in all four.

With James Nickel’s latest masterpiece he has given mathematics, publishing, discovery, and think-tank worlds a contribution to which all teachers, students, thinkers, and generations will point. No one has both the breadth of knowledge combined with the educational practice to match Nickel’s curriculum. No one ever needs try again.

The Church, the school, the academe, the world should sit up and take notice. Mathematics reflects the language The Father used to create the universe; its principles and truths permeate all of life, every problem, and solution. Jesus, second person of The Trinity, the God-Man, is the source, unification, sustainer, and will be the culmination of all truth. The Spirit now amplifies creation’s message to every one of God’s creatures: “Look! See! Know! Math is God’s witness to earth from Heaven!” All mathematical knowledge throughout creation is intended for Trinitarian glory. James Nickel has held a mirror up to mathematics to announce The Personal Eternal Triune Creator’s lordship over all.

Dr. Mark Eckel, President, The Comenius Institute, Indianapolis, Indiana

APAC 2018: Service-Learning and Statistics

Screen Shot 2018-07-20 at 1.36.45 PM.png

This week I am leading a workshop at the 2018 AP Annual Conference on “Statistics and Service-Learning” in Houston, TX. The talk is on integrating service-learning projects into AP Statistics curriculum, specifically with the goal of impacting students on an affective level.In addition to the resources that you will find below, feel free to check out some of the prior posts on service learning:

ABSTRACT:

This session will equip participants to design, implement, and evaluate AP Statistics service-learning projects in which students partner with nonprofit organizations in their local community. These projects synthesize the major concepts of experimental design, data analysis, and statistical inference in the real-world context of community service. Through these projects students integrate their conceptual understanding of statistics with the practical functioning of their local community, ultimately gaining a deeper appreciation for the role of statistics in the organization and evaluation of service societies.

PRESENTATION:

You can click the image below to find the PowerPoint that accompanied my presentation.

 

Screen Shot 2018-07-20 at 1.40.54 PM.png

For many of the service-learning projects that my students have completed I am indebted to the willing partnership of Mobile Loaves and Fishes. Here is some introductory information on this great ministry:

Community First! Village Goes Beyond Housing for Austin Homeless, from the Austinot

10 THINGS TO CONSIDER BEFORE IMPLEMENTING A SERVICE-LEARNING PROJECT:

The following are the foundational questions that you as an instructor should consider and reflect upon prior to implementing a service-learning project. This list is not meant to be chronological though some aspects will naturally precede others. Start by considering the course learning objectives and your method of assessing those objectives and then go from there.

1.What are the major learning objectives/big ideas/enduring understandings for your course?

The purpose of the AP course in statistics is to introduce students to the major concepts and tools for collecting, analyzing and drawing conclusions from data. Students are exposed to four broad conceptual themes:

  • Exploring Data: Describing patterns and departures from patterns
  • Sampling and Experimentation: Planning and conducting a study
  • Anticipating Patterns: Exploring random phenomena using probability and simulation
  • Statistical Inference: Estimating population parameters and testing hypotheses

2. What are real-world situations where students can apply the concepts studied in your course?

  • Identifying a non-profit service agency which requires survey research (program evaluation, client needs assessment, etc.)
  • Students develop a survey instrument, conduct survey, compile and code data, analyze data, present results

3. List some potential community partners along with some basic descriptors that may impact how your students work with each partner (ex: What is the size of the organization? What issues does the organization address? Is the organization non-profit, governmental, religiously affiliated? Etc.) In lieu of a partner organization you can also consider a general community need for students to address. List some general descriptors of the project involved in addressing this community need.

4. Look for potential matches between organizations on your list from question 3 and your responses to questions 1 and 2. If there are multiple potential matches then consider the pros/cons of each and list them. Be sure to recognize how your matching affects the organization of the project (large scale as a class v. small scale as groups), which in turn may affect your response to question 5 below.

5. Once you have begun narrowing potential community partners that offer opportunities for students to interact with course content, consider how will you assess students? What will be the final product? What expectations will you have for students throughout the project and how will you communicate that to the students?

6. How will students be organized to meet the objectives that they will be assessed on? Will students work as individuals, teams, as a whole class?

7. How will students be equipped to complete the project successfully? What will they have gained from the course up to the point of assigning the project that will aid them? What additional tools/skills/knowledge will students need as the project proceeds?

8. What will be the timeframe for the project? How will students be held accountable to the timeframe? At what points will students receive feedback on their progress?

9. Why should students care about the project? What will you do as an instructor to get student buy-in on the project?

10. How will students reflect throughout the project? What opportunities will you provide for students to pause and consider the work they have done?

HANDOUTS:

From my AP Statistics Project 2018:

Screen Shot 2018-07-20 at 1.57.49 PM

(Clicking the image above will take you to the students’ final presentation)

From my AP Statistics Project 2016-17:

Screen Shot 2016-06-29 at 1.09.07 PM

Screen Shot 2016-06-29 at 1.10.27 PM

From my 2015-16 AP Statistics Project (Organized as an entire class project over the full year):

From my 2014-15 AP Statistics Project (Organized as small group projects in the spring semester):

*NOTE: some documents above were also used in this project, either in the form in which they are posted above or in a slightly modified version

EXTERNAL RESOURCES: