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)

????

Promotional administrative positions as a career pathway for teachers

Administrative positions are seen as a career pathway for teachers. For two years I have said that this is a grave problem in the teaching system

a) It takes good teachers away from the classroom
b) These positions tend to rapidly turnover causing inconsistency in BMIS application
c) There is a vast gap between managing staff and managing children
d) Salary discrepancies cause dissatisfaction between teachers and those aspiring to higher salaries

L3CT causes similar issues
a) Only those with large amounts of time can produce the documentation required
b) It tends to inspire teachers to create a load of meaningless and ill-advised programs that are unsustainable and poorly implemented to satisfy L3CT criteria
c) There are clear issues over the values of L3CT criteria with the change away from developmental programs and back to direct instruction in support of gaining improved NAPLAN results

Where is the encouragement for good teachers to actually remain in the classroom and teach, or guide and mentor developing teachers (not just practicum students)? Why would you train new teachers if they will be competition for these aspirant positions? Can L3CT actually encourage teachers to stay in the classroom?

Once upon a time, teachers progressed through their classes and were given intellectually more challenging classes as time passed - growing their management skills through to HOLA/HOD (managing staff and students) and then progressed to Deputy and Principal. Those unable to make HOLA/HOD/Year leader work, would not get access to Deputy and similarly Principal. This system made sense. Hopefully if you weren't a good teacher, good manager of students and good manager of staff you would not get promotion.

This still applies in our older leaders (who also today have to be capable fundraisers and business managers) - but some of our new leaders that have devalued the classroom (many openly say that they hated teaching and wouldn't do it again) may be great at managing individual students but have forgotten the other side of the job (managing one student is not managing their behaviour in the classroom or their effect on others!).

I loved the idea of classroom first, but sadly now - it has just become another bit of rhetoric. We are now starting to base classes run each year on class sizes rather than need for providing opportunities for student excellence (lets hope that the error in this logic is quickly rectified!). We put students in classes that they will succeed in (even though potentially below their ability) to avoid poor graduation scores or TEE results being put in the newspaper.

We ignore the fact that our kids are excelling in individual fields and beating all rivals and bus them to other schools for higher subjects or give them distance learning "opportunities" rather than reward them for sticking it out in a low socio-economic school and being given their deserved small class advantage.

It's something that deserves further consideration beyond any budget issue as it is a case of equity for these children. We always worry about the financially challenged low achievers, but we need to consider that schools are places of learning foremost and our high achievers (whether teachers or students) deserve our support too.

Graduation presents

One of the nice traditions at school is for teachers of year 12 students to purchase the subject awards.

The usual items tend to get bought: pens, shopping vouchers and the like.

This year we found one item that I loved. One of our quirky students was given as part of her package (our Discrete Mathematics subject winner), Dr Seuss' Places to Go.

The prose is remarkably apt:

"Congratulations!
Today is your day!
You're off to Great Places!
You're off and away!

You've brains in you head.
You have feet in your shoes.
You can steer yourself
any direction you choose."

Another maths student was given Rich Dad, Poor Dad which outlines the difference in financial education parents provide based on whther they have/haven't amassed wealth. It's a great book.

Another that I thought of later was the E-Myth, a book about Entrepreneurialism. The E-Myth and Sun Tsu's Art of war heavily influenced my early business life.

Mr Men books can also be a source of inspiration as they describe so many personality types.

I like the idea of books as you can personalise them with an inscription - and they tend to be kept. One of my teachers gave me a battered copy of Catch 22, I still have it and read it from time to time.

Staffing issues

There's nothing like managing staff. It's a royal pain in the ... No matter what you do you can't please everyone.

There are two main methods I've seen.

a) By the book.
b) With a wink wink.

By the book is the way I always did it. Of course, since it was my book, it was easy. If I didn't like the way it was working I just changed it. Administrators tend to run organisations like this. The crux of it being successful is ensuring quid pro quo occurs and extra effort is acknowledged and rewarded in a way suitable and public for both parties. The less flexibility in the rules, the greater the opportunity for dissatisfaction by those going the extra yard as there is little opportunity/recognition for reward. Over flexibility lends itself to abuse (the situation around L3CT and L3 Admin promotion is typical of this situation).

With a wink wink, is a very popular method. It involves being pally with staff and telling people or groups they will be looked after.. nothing on paper, "just wait and see, it will be ok". This has never been my favourite but often can be used to defer a decision until a point that is more advantageous to the organisation than now and relies on favours/corruption/back scratching. To my mind this is an unprofessional option (I like to know where I stand) - it is usually coupled with "being part of a family" or with "unofficial" perks that are secret from other staff. Staff performance/ability/performance is often of little relation to staff hierarchy. Entrepreneurs tend to operate like this, wringing the last cent or skill out of staff through unfulfilled promises. It has no real appeal to me, but for staff that like the warm and fuzzies/charismatic leader it is quite effective. Many people on temporary contracts have felt the rough end of this recently, being laid off or transferred due to the half cohort despite varying assurances.

Time to reflect about past students

The year 12's are starting their TEE exams next week, and we are all thinking about them. For many, schools have invested hour upon hour getting them ready for the highest stakes exam of all.

Seeing them graduate gives teachers a lift but I am surprised at the lack of middle school involvement in graduation ceremonies. Once passed to the senior school, their job done, that whole relationship built upon over two years is released and left to whither.

I think this could be seen as a failing of the middle school model - in an 8-12 model this sort of relationship continues to be built upon over 5 years and can be a significant part in a student's life.

I wasn't going to the graduation ceremony this year, but I changed my mind at the last moment. I'm glad I did, seeing the kids at their finest hour, at the culmination of 12 years work is not something to be missed.