Jim Hogan’s Mathematics and Statistics Course • V1

Overview, Welcome and Introduction

Do you have problems with maths?

This course is for teachers, or anyone really,  to review understandings and learn or be reminded how Mathematics and Statistics works. There are some key and deep understandings that drive being confident and enjoying Mathematics and Statistics to solve problems. This is the essence of this course. Difficulty? I rate it as pretty straight forward.

The Self Assessment Anxiety Meter

Rate Yourself - This data is not collected. It serves only for you to reflect.

The fear of mathematics called “math anxiety” is a now a common modern day manifestation. Typical indicators include “I was not good at maths”  along with “a feeling of repulsion” or that “Maths is too hard” when presented with a situation involving numbers and mathematics. This course also aims to overcome this negativity. Everyone can be empowered to enjoy mathematics. The more mathematics you know the more mathematics you will use.

Traditionally mathematics has been taught from a text book and involves learning a new idea and then practicing that idea by working through a structured set of exercises. These typically increase from easy and guided to more “figure it out yourself” problems. This procedure has been at the core of education in middle to senior school and even at university level for a long time... centuries. This approach also remains a very secure way to learn about mathematics for many. The approach also caused math anxiety when teachers moved on to quickly for some learners. Building robust stepping stones for future knowledge and making connections is vital.

There is one really important point to make about learning pretty much anything. You have to engage. That will mean actually figuring out something. Time to ponder and reason logically to make sense of the problem. Many of my colleagues agree that a pencil and paper is the way to learn mathematics. Understand the problem, draw it, read it, restate it, develop a strategy and do the work to see where it leads. That is pretty much what Polya said years ago in his book "How to solve a problem." All relevant today as it was in 1945.

This course is not set up as a traditional book. The author, Jim, has no intention to try and write another “text book”. There are many excellent textbooks already available and there are some dreadful publications as well! The tasks in this course vary in difficulty but always make connections and test ideas. There is email contact and help available to help progress through the canyons and quagmires.

A Reward
A certificate will record successful completion of the course. There are no grades or judgments. A certificate will mean I, Jim, am comfortable that you know enough of whatever was intended. The level is about NZC Level 4/5, with journeys down and up a little as well.

 

A section will give you credits. Some sections are more involved and will require more thinking so the credits will vary a little per section.  Gaining 20 credits or more across all sections will mean this course has been successfully attempted and will make me (Jim) write a follow-up course. The interaction I have with you will inform me of your understandings.

There is no charge to access and undertake this course but a $10 fee is asked for to cover admin and my time in each section if you want to gain credits and eventually a certificate.  A ten section course certificate would cost $200 and would represent about 100 hrs of thought but that might vary from person to person.

You would need a computer, browser and and email account. You will also need a calculator, a pencil or pen and some paper. The usual mathematics equipment, a ruler, compass and setsquares, protractor might be useful as well. You could use a spreadsheet and a graphing calculator .app on a cell phone or a more sophisticated package like Geogebra. No need yet, that will just frighten you.

What will you learn?
Key ideas underpin mathematical thought and the many connections that can be made between them is where understanding happens and is realized. There are skills that need to be mastered and basic knowledge that has to be remembered. Understanding is a very different ball park and is where application happens and genuine problem solving occurs.

 

What is a “problem”?

 

Learning how to expand an algebraic expression such 2(x+3) is an exercise. Text books are full of endless lists of exercises. Not a single one of these is a problem however. Likewise, doing “Numbers” is very different from doing “Mathematics”.

 

Add 2 and 39 to find the total is not a problem. This is "doing numbers".

 

An example problem is asking “How many handshakes happen when a group of 12 people meet one another?” Another example is “How likely is it for the chicken to make it across the road?”

A problem is a situation and a question for which no suggestion is given about how to develop the solution.

Be aware, it is better to solve a problem in 5 ways than to solve five problems!(Polya 1945).

Problems almost always involve clarifying what is actually being asked. In the handshake problem we probably need to know that each person will use a hand and everyone actually has at least one hand. In the chicken problem we need to know a few things about the road, what the traffic flow is and how fast the chicken can run. The handshake problem has a single answer but the chicken problem has many.

A Last Note
Having fun with mathematical ideas is important as well. Mathematics is a human construct and something that should be enjoyable. Fun is part of this course. Mathematics has very practical applications in everyday life for everyone but in a grand diversity of ways. Again, the more you know about mathematics, the more you will use it.

 

Mathematics and Statistics are a related and both will often be referred to in this document as Mathematics.

 

A final anecdote. After what seems like 720 years of being in a classroom teaching mathematics, physics and computing and another 500 or so years helping teachers as an advisor I confess to asking all the wonderful past students whom I bump into  “What do you remember about the classes I taught? Do you remember the maths, the physics?” The usual answer is “I only remember we had a lot of fun. Thanks.” Thanks to all my past students also. I learned more than  you did!

So to my new students, have fun and ask every question.

Jim Hogan
July 2021