This 6 week online course presents a conceptually-based approach to teaching mathematics and uses the straight-line coordinate geometry unit in which to do this. The course utilises GeoGebra. However, other dynamic geometry software or indeed, no dynamic geometry software, may be used. The success of this engaging, conceptual, inquiry-based approach lies in the fact that during the first few lessons students learn to perform the following skills without utilising formulas: read gradients from straight lines, sketch straight lines directly from equations (without using tables of values), read an equation directly from its graph and find the midpoints and distance between pairs of points. Students who struggle with Coordinate Geometry tend to achieve far greater success and confidence with this approach. At the end of the unit traditional formulas are derived and then employed. The December date enables the course to be completed during the holidays, finishing early Term 1. Accredited PD Hours = 7
Secondary Mathematics Teachers
A normal online course is delivered over 1-12 weeks and is worth from 3-12 PDhrs depending on the course content and its objectives. Participants will not need to take time off, the course date is the START date only, end dates will be advertised with course hours. Learn more HERE.
The course can be accessed 24/7 over a 6 week period. Due to the requirements of self-reflection and the implementation of strategies, participants will need to spread their involvement evenly over at least 3-4 weeks of the 6 week period.
The December occurrence runs through the Christmas holiday period, ending early Term One. Participants are able to work on the course whenever it suits them during that period.
This course contributes to 7.0 professional development hours.
There are no occurrences of Online - Individual in Australia (NSW) at this time.
(Article, video, forum post) Welcome to the course; meet your facilitator; course requirements explained; reference to Professional Standards; Technical requirements explained; the introductory forum.
1 hour and 30 minutes
Unpacking rules-based teaching: The traditional approach is explained as a juxtaposition to the conceptual approach; participants share their views (Article, forum post).
Unpacking the conceptual approach: the conceptual model explained (Detailed teaching resource, video).
Prerequisite GeoGebra skills: The GeoGebra skills required for the course files explained (video, Participation).
Phase One unpacked: Participants to work through one of the Phase One real world activities (Participation).
The Socratic Method (Articles, past posts,forum post).
Phase Two unpacked: Phase Two enables students to ascertain gradients, y intercepts and straight line equations without the use of formulas (Videos, GeoGebra file, past posts, forum post).
The Brick Wall Theory explained (Article).
Phase Three unpacked: (Article, videos, exploration of Phase Three questions, GeoGebra file, past posts, forum post).
1 hour and 30 minutes
Phase Four unpacked: establishing the formulas, the case against compartmentalisation of mathematics instruction, 30 minutes exploration of Phase Three Activities (Articles, GeoGebra files, participation).
Dealing with student spread within a unit of work (Article, past posts, forum post).
Phase Five: Simultaneous Equations (Video; article).
Phase Six: Moving away from y = mx + b - (Article).
Phase Seven: Parallel and perpendicular line relationships (Video, GeoGebra file, Exploration).
Phase Eight: General form of the equation of a straight line (Article).
Brick Wall Forum (Forum Post)
Student assessment options (Article, videos, assessment rubric docs, past posts, forum post).
Student engagement example - (Article, video, Prezi).
The completion process.
Optional extra: Dealing with Student Networked Computers Teaching students with networked computers, Considerations, Training students to follow a network protocol (Articles)
Please note the feedback listed here is unfiltered, and includes all comments and ratings collected.
Many parts of this course were affirming as they followed my general
teaching practice. Other sections stopped me and made me reconsider how
I was presenting material to my classes. I love the examples that you
gave – both on geogebra and through the video on assessment. Time will
always be an issue and I am not sure if all topics would be best taught
this way. An ongoing discussion within me!
At times I did feel I was repeating myself in my posts, but it
certainly caused me to reflect on my teaching practices. I had
difficulty opening some of your documents at school as we are blocked
from some of the google sites.
I enjoyed the course. It let me work at my pace since it was online.
The delivery of the course was excellent.
This course has opened my eyes to understanding a different
approach to teaching Maths. I have always felt the need to break away from formula driven teaching and find alternative methods for creating understanding, and this course definitely touches on some very effective strategies.
It took a while for me to get used to the site. But once I find out how to go to the course schedule it was easy to navigate.
I thought the course was very interesting and was well presented and well resourced. It had some excellent ideas on how to deliver a better message to students struggling with co-ordinate geometry. I can also see how similar messages can be delivered in other areas.
This is fantastic course. I liked every single phase and learned lots. Even though my students are loving Geogebra.
Overall, I really enjoyed doing this course. I got so much out of it. I am already starting to incorporate a conceptual approach into my teaching. I can’t wait to do more with Geogebra with my classes.
I especially liked the way that Richard used the Socratic method, in conjunction with Geogebra, to help the students learn and understand what the “m” and the “b” mean shown various graphs of “y = mx + b”. And the implementation of “brick walls” along the way, e.g. horizontal line equations, was well done.
The U.K. video on the teaching of straight line coordinate geometry got me thinking to how I might use this approach when teaching different types of curves, e.g. parabolas, hyperbolas and cubics.
All in all, a wonderful course!
This course not only increased my capacity in using GeoGebra but also allowed me to think about the teaching of mathematics in general. Using the conceptual approach, coupled with socratic questioning, is a powerful tool in building knowledge, independence and confidence in students.
Found this course challenged my current thinking on content delivery. It affirmed the practices I was developing individually. Now inspired to keep going.
I found this course really useful as it sparked quite a few ideas outside of coordinate geometry as well. The longer course time gave me the chance to think about what I had seen over a period of time and apply it in small bits and pieces. Some really good resources as well.
The course gave me lots of food for thought on how to deliver a co-ordinate geometry unit conceptually though I wasn’t completely sold on the Geogebra aspect of it I think I will continue to try to learn more about it.
The course was a very comprehensive insight into conceptual based learning.
Very pleased I did this. Not only did I get some great resources I can use with my classes right out of the box, but the thinking involved in getting the students to learn through asking questions and structuring the classroom environment differently were very good. I’ll have plenty to chew on for a while.
I liked how I could go at my own pace and that it provided excellent practical and usable strategies to assist me in ensuring that my teaching of the coordinate geometry topic was engaging, as well as ensuring information was retainable in the long run.
Excellent, Richard is a great mentor and very supportive, the feedback was constructive and helpful. The delivery impeccable and the content awesome.
A very worthwhile course to undertake from both a conceptual approach idea, as well as a great use of the geogebra program as a learning tool for the students.
The delivery aspect of this course was really fantastic and the presentations from Richard were great. They were very easy to understand as an online presentation. Furthermore the online presentation allowed for an individual teacher to access the course as they were able to manage the time and this was particularly helpful for me.
My comment on the course has been posted in the forum within the course. The course was very useful and interesting. It was conducted very efficiently with the responses being prompt and specific. I enjoyed the interactions during the course and some of the strategies discussed were eye-openers. Thank you for the course.
A fantastic course, insightful, inspiring, great resources and a fun way to teach coordinate geometry! Great feedback from Richard and very personal.
Great, enjoyed the flexibility.
I found the course informative and thought provoking. I am pleased to have been introduced to Geogebra.
Richard has taught in 3 states and territories of Australia over the past 25 years and has been Head of Mathematics at Oxford Falls Grammar School for 6 years. He has developed a teaching style which is interactive and relational, directed yet open ended, and which fosters individual progression, higher-order thinking, and collaborative learning. Richard is a passionate campaigner for conceptual learning; his professional journey continues to lead him to discover more and more ways of teaching mathematics conceptually and he delights in sharing these with other teachers.