Teaching Surface Area

I've been examining the issues with teaching surface area.

Here's an approximate sequence:

Prior knowledge required
(easily takes 3 weeks+ yr 10 with a weak group filling gaps)

• Notation for parallel and perpendicular sides
• Perimeter of Rectangles, Squares, Triangles (with all sides given)
• Area of Rectangles & Squares, Triangles (with all sides given)
• Circumference and Area of circles
• Area of Trapezium, Sectors
• Area of Composite Shapes (with all lengths given)
• Area of Composite shapes (finding missing sides using subtraction)
• Area of Composite shapes (using ratios of the area of known shapes to find area eg. 1/2 circle)
• Arc length
• Pythagoras, Trigonometric ratios
• Area of Composite shapes (using Pythagoras & Trigonometric ratios to find missing sides)

Surface Area Topic

• Identifying 3D shapes (cylinders, spheres, pyramids & prisms)
• Constructing 3D shapes using Nets (cylinders, pyramids and prisms)
• Identifying cross sections of 3D shapes
• Finding the area of cross sections of 3D shapes
• Finding the surface area of simple 3D shapes using defined formula (cylinders, spheres, pyramids and prisms)
• Using surface area of simple 3D to solve composite surface area problems (and using subtraction to subtract shared hidden sides)
• Deconstructing 3D shapes into constituent 2D shapes
• Finding the surface area of composite 3D shapes using deconstruction and 2D shapes
• Finding surface area of simple 3D shapes that have had sections removed using ratios
• Finding the surface area of composite shapes using simple 3D shapes, deconstruction and ratios.
• Using Pythagoras and Trigonometry with planes in 3D shapes to find surface area

It's a big topic!

Favourite teacher

I had a student once say "you're my favourite teacher" so I said to him, "I'm a maths teacher - is there a) something wrong with you or b) do you want something?"

I did ask him why and he said, "I can do the work in your class". This class was special as we had halved its size by splitting it between two teachers during the quiet period after the 11's and 12's finish. I'd been given the students that had potential but were struggling or that were destined for courses with low maths requirements. I'd been pretty strict with them in the first two weeks sending some off to isolation, having a number of one sided discussions with the boys, a few BMIS' and a few blue letters to parents.

There's nothing here that would make a student like the class. Yet, I sat back and listened to the student. In fact he went on to say that in other classes he went from 'bored because it was too easy' to 'giving up because it was too hard'. They had come from a class with a very popular teacher that had consistently good results, so I knew it was a student issue.

I explained to the student that in a smaller class it was easier for me to tailor the lesson to his optimum speed of learning - get on his back if he was loafing, fix his errors in a timely manner and acknowledge his successes. He had to work on his resilience too, and had to try more before giving up!

He understood that. I'd go on to say that when classes are getting feral or unmotivated, splitting them and resetting them into smaller classes is a legitimate and positive strategy.

Another yr 11 student at the end of the same day said that he liked our school because the teachers really cared and were willing to spend any amount of time outside of class to fix a problem. I like that students in our school are willing to spend inordinate amounts of time outside of class identifying and fixing up issues in their understanding. It can get a bit wearying sometimes on a full day. I have seen in another school "maths club" work well, where knowledge or skill issues are corrected in a math teacher overload situation (often 5 students to one tutor). This could take some pressure away in the earlier months of the year and give access to alternate learning sequences for topics.

I do love this end of year when we can consider our teaching practices, do some experimental class arrangements, have extra time to spend with students and test ideas for motivating students.

Striving for excellence vs achievement

I can think of four models for a school. These ideas underpin curriculum and pastoral decisions. Where a school understands its direction, it can drive staff and students accordingly. It is the major theme that governs the mission of the school.

Education based on excellence and opportunity (education driven)
School as a place where students strive for excellence - sights are set high and achievements on the way are celebrated. High expectation drives this system where teachers have to remind students of their successes whilst they pursue ever higher goals. Schooling is an esoteric activity - one without goals other than higher learning. This is a system driven by opportunity for education.

Education based on success (success driven)
School as a place where students find success and gain self worth. Students are only given situations where they are successful. A raft of factors is taken into account (the whole student picture) rather than just their intellectual capability to ensure students will succeed. This is a system driven by the need for further success.

Education based on vocational needs (workforce driven)
School as a place that provides key skills for the workplace. Students are streamed into interest areas and delivered to the workforce and tertiary providers already along a workforce pathway. This is a system driven by workforce needs.

Education based on student readiness (student driven)
School is a place that attends to individual student needs and presents information at a pace best suited to the student. As the student becomes ready for the new content, it is provided in a timely manner. This is a system driven by developmental readiness.

I think the success based schooling is based on an ill advised premise as motivation cannot be maintained on perpetual success. Success is only valued if the risk of failure is real. This is the same issue with the developmental approach. This is one reason why the entertainer rather than teacher is so necessary to maintain discipline in classes in WA where these two systems are the most common!! (without risk of failure and vague BMIS alternate measures are required to keep students on task).

Similarly, the vocational needs approach is subject to the vagaries of the workforce and naivety on the part of students and their career goals. To stream students into a career too early is to pigeonhole them and limit their future success without complete retraining. Motivation falters as students find their chosen field to be real work.

The whole Australian way was based on the fair go and the battler. Without the battle or the ability to get a fair go(opportunity), we are changing national ideals. Excellence and opportunity (with all it's inherent failings especially for unmotivated and/or low ability students) is still the better of three evils for the majority of students - with limited pockets of students where the other methods can have sensational results.

Small classes and NCOS

Small classes in public schools have been an bone of contention. The "no classes less than six students" policy caused a lot of angst when considering how to deal with talented students since it was impossible to offer small classes to cater for them.

It would be interesting to know how smaller schools are dealing with this issue. Are they:

• redistributing these students into easier subjects (indicators could be increased enrolments in easier subjects or decreased enrollments in more difficult subjects across all schools)
• ignoring the directive and creating small classes (indicated by small classes running)
• reducing the number of subjects offered in year eleven (indicated by examining the number of different NCOS classes offered in year 11/12)
• increasing the number of students using distance education (indicated by an increase in SIDE enrollment numbers in metropolitan schools)
• moving students across schools (indicated by an increase in transfer numbers either as temporary busing or permanent transfer)
• moving talented students into centralised scholarship or G&T programs (indicated by examining enrolments in G&T programs)

????