Scratch and the Maths challenge

My daughters do a maths challenge each week at their primary school.  I didn't pay much attention to it until my youngest was worried that she wasn't improving.  My usual criticism of these weekly quizzes is nothing is done with the information and students keep getting the same questions wrong.  In many cases, the reasons why they are getting questions wrong is never investigated.

So I had a look at the challenge and it focused on addition, subtraction and times tables.

I wrote a little application in scratch to help develop some basic numeracy and help identify where issues were occurring. I added in extra steps to assist where we found issues and practice was needed (with instant feedback).

It covers:
a) learning multiples
b) adding/subtracting to and beyond 10
c) tables (using commutative property and division)

You should be able to see it below.

Assigning classes to teachers and Performance Development/Management

One of the roles of a HOLA is to assign classes to teachers each year.  Constraints limit putting the strongest teacher with the optimum class with optimum defined as the class with the highest potential for learning.

Constraint 1: The timetable

The timetable often limits which teacher can be placed in which class (eg. teaching the same course to two different classes).  This is common where ATAR and General classes are run at the same time to assist with students moving courses midstream or where streaming is done, allowing student to move stream without disrupting other subjects.

Constraint 2: Experience vs capacity building

An experienced teacher understands the scope and sequence of a course of work, has strategies evolved and resources collected.  An inexperienced teacher requires opportunities to develop their skills.  Some staff have some specific skills (Specialist, Foundations, low ability, extension, leadership) that make it desirable to put them in a specific course.

Constraint 3: Part time staff

Some staff are hired on the basis of being part time to fulfil a specific need or have a circumstance that requires a part time approach.

Constraint 4: Capability / Capacity

In some cases, staff have limitations that result in being unable to take certain courses.  Similar to constraint 2, some staff lack the confidence to attempt ATAR courses, Year 12 courses, lower school courses, classroom management limitations.  Teachers may be unable to dedicate time required to support upper school classes or to develop capacity to deliver upper school classes.  

Constraint 5: Personality/Cultural conflict

As much as I would like to say Professionalism should overcome this constraint, this is not always the case.  With enough flexibility, interaction can be minimised to promote a functioning department whilst performance development works through the underlying issues.

Constraint 6: Stage in career

Teachers have different requirements at different stages in their career.  The impact of supporting their own children, generational gaps towards retirement, graduate opportunities, caring for parents, seeking promotional opportunities, seeking higher learning will impact on how a teacher is deployed.

Once the constraints are considered, the approach used to assign classes needs to be considered to maximise learning and staff morale.  I have primarily used three approaches or combinations of these approaches.

A: Best teacher for each class (seniority model).  

Capacity building occurs as staff vacate desirable courses.  Staff are allowed to remain in courses for significant periods to develop a thorough knowledge of each course. 

Advantage: Optimal learning for students (most capable teacher aligned with suitable classes). Fewer parental issues regarding teachers developing capacity. Mid tier classes may get higher levels of support (as teachers develop capacity/demonstrate a teacher's suitability for more desirable classes). 

Disadvantage: Can become stale, transition can be difficult in case of promotion, entitlement issues, sickness, etc.  Some teachers will have a set of less desirable/higher behavioural requirement courses causing morale issues/higher turnover of new staff.

B: Balanced approach. 

Cycling teachers through courses developing capacity across the entire teaching group. 

Advantage: Flexibility in case of changes required due to turnover.  Higher morale as teachers develop their capacity in a transparent manner. 

Disadvantage: Ongoing suboptimal learning whilst teachers develop capacity. Higher turnover as teachers seek positions with lower levels of change required.

C: Allocating points to courses.  

Each course is allocated a point in a distribution.  The average of a teachers subjects is allocated with an aim for teachers to have a combination of challenging behavioural classes and challenging academic classes. 

Advantages: Transparent, seen as a fair approach for teachers. 

Disadvantage: Sub-optimal learning, teachers focus on desirable classes and sacrifice attention to less desirable classes (eg. upper school vs lower school classes, academic vs less academic classes etc).

D: Cycling teachers with students.  

More common in pastoral care situations.  Can be combined with A/B/C.

Advantage:  Students become familiar with teaching pedagogy and teacher becomes familiar with needs of students.

Disadvantage: Conflicts may be carried over extended periods.

Why the Classpad was a monumental mistake.

When the Classpad replaced graphics calculators, the thought was that it would drive a new level of applied mathematics, removing from students the repetitive parts of problem solving, widen access to higher mathematics and allow students access to deeper learning.

It failed.  It just produced a level of IT complexity irrelevant to mathematics and little further development of mathematical thinking.  The proposed gains in graphing did not materialise (due to the size of screen and accuracy of the LCD) and the CAS element was nifty but questions it could be used for were often implemented in non calculator sections anyway and calculator section questions often have to avoid questions that would otherwise demonstrate understanding but can be answered without knowledge by the calculator. In many cases it caused issues for examiners to ensure that problems were not trivialised by button pushing.  

The level of skill with the calculator by each teacher has the potential to differentiate between students in classes and schools more so than their individual mathematical aptitude (or teacher knowledge), particularly in Applications and Methods as teachers in rotations develop their skill with the device.  It was never the aim to have the calculator impact on the teaching quality received by students, but as each new teacher is introduced into a course, it has increasing potential to do so, more than without CAS.

I don't  think it has aided algebraic ability either, with students not always receiving the algebraic grounding developed through solving complex equations.  CAS has the potential to trivialise this process, and can limit the development of fluency, particularly where texts do not state where it should be used (or where students use CAS where they shouldn't).  The counterargument is that this is dependent on the skill of the teacher, and I don't discount this, but it is just another factor that impacts on teaching with limited, if any, benefit.  It certainly hasn't given access to maths at a higher level than ever before, one only has to look at declining engagement numbers and the relative farce that is the current applications course. This though, is just my opinion.

It is now predicted to cost $270 per calculator, which tied to texts, revision seminars and revision books typically used by students can top the booklist for Methods and Spec to be over $500.  It's an equity issue I raised with Rom Cirillo (who I respect greatly), who indicated it was a factor that had to be controlled by HOLA's, something that we all have to keep in mind, especially in low SES schools.  Increasingly, where Maths was once accessible by all, the combination of the increase in literacy requirements (through an increase in statistics) and CAS calculator usage (leading to more "applied" literacy type questions) change our subject to a further limited demographic. 

This is causing some students to reconsider doing higher mathematics, or worse still attempting to do it without the calculator, particularly if it is lost or broken (and not covered by the one year warranty).

I've just had an email from Abacus that they are getting a 15% increase in cost next year.  At $270+ it is getting pretty close to the cost of a reasonable tablet, with a larger screen, multi-purpose, similar software and enough battery life to get through a day.  Sure, standardising it for exams would be difficult but considering it as a thought exercise it makes you think.

Universities and other learning areas never took the CAS calculator into their courses making it irrelevant post schooling.

If it is costly, is not providing the benefits suggested in senior school classes and has little relevance post schooling, would we not be better dropping it as a failed experiment.  I remember reading a post from Charlie Watson (Calculator guru and all round nice guy) proposing to discontinue it.  I do agree and would like to see a pure math subject returned where the skill in developing mathematical knowledge through a simple text and a teacher was the primary objective rather than driving the use of a mediocre device with limited applications beyond high school.

Course Counselling and Mathematics

The current Mathematics course is not my favourite of the past few editions.  

It has four main courses: 

- Foundations (for students that require basic numeracy)

- Essentials (for students to develop their basic numeracy to a TAFE level)

- Applications (for students to develop skills for higher learning)

- Methods (for students seeking maths skills for tertiary math/science courses)

and a fifth course Specialist that can be taken in addition to Methods (for those seeking to complete Engineering or Mathematics courses at University without additional courses to bridge to the level required)

Unfortunately WACE and University entrance is the main reason why the majority of students take Mathematics courses.  I would suggest that seeing Mathematics as only a pathway to higher learning or graduating high school is a very limited view as it does not consider the requirements after entry to a learning institution and for lifelong learning.  

The difficulty gap between Applications and Methods is large, much larger than in the previous iteration of ATAR courses (2AB/2CD 2CD/3AB 3AB/3D) as the option to do 2CD/3AB no longer exists.  The mean for Applications is 55, which results in half of the students sitting the course not having scores that is conducive to a university entrance score.   Given this is the case, half of these students end in TAFE or using other courses to build their ATAR score.  Getting a 1st or 2nd ATAR score with Applications is unlikely (and when done, tends to be students that drop in from Methods in Year 12.  Given this, as a counsellor, if I was unsure about whether a student should do Methods in Year 11, I would counsel them into Methods and parachute them into Applications if they were unsuccessful in Year 12).  This makes choosing Applications a problematic choice for many students (why do it if there are other subjects that I am more likely to gain a score with).

The mean for Methods is 65 with a SD of 12, with 3/4 of students getting a scaled score above 55, indicating that this is a course to build a reasonable ATAR score around. If students have the ability to do Methods, they should.  If they wish to do a Science based course, this is the only option to gain the thinking and capacity required for Science courses.  They may not use all of the Maths, but they will gain skills invaluable for learning new content beyond their current understanding.

The difficulty of Specialist has reduced its importance over time for maximising ATAR scores as the effort required is often better put to ATAR English, Chemistry, History or Physics and is only done by those with a passion for Mathematics.

My frustration with the current counselling thinking is that because many university courses do not have Mathematics pre-requisites, that it is better to do Applications (and pass) than Methods and potentially fail or that if students have C's or D's in Maths they should bypass Essentials or Applications and do other subjects instead.

To this I would simply say - Mathematics is about lifelong learning.  It is more than just entry to tertiary education.  There is no point gaining entry to higher learning, to only fail (or have to do bridging courses without the assistance available in school when you get there).

Doing Specialist puts you in an elite group of people able to do something that the majority of people cannot do.  Putting yourself in an elite is never a bad thing if you have the ability to do so.

Doing Methods takes effort, but is an opportunity to stretch yourself and truly learn how to learn. It will help a student get to university in the majority of cases if they have shown the aptitude in previous years.  If you complete Methods, you are likely to be a competent Mathematics student at university.

Doing Applications will develop your mathematical skills to a level that will mean in the majority of cases you will not need to learn more mathematics in later life but is unlikely (in at least half of all cases) to assist with University entry.

Doing Essentials will help you reach the next level in Mathematical understanding.  You will better understand the world in which you live from a basic numeracy, financial, measurement and statistical perspective.

Doing Foundations will raise your basic understanding of numeracy to allow you to function in society.

From a school point of view Mathematics provides opportunities in senior school to exploit 4 years of learning in lower school and has a course for any student - more so than any other subject (I'm looking at you English and HASS!!).  It is cheaper, more flexible and easier to run a full Mathematics course than 5 elective subjects trying to cater to various needs and ability levels under-subscribed.  A lesson learned by a few schools I dare to think.  Not making Mathematics compulsory results in significant bloat in school offerings.

To get students to choose Mathematics willingly requires many years of work.  Students must have an understanding that they will be supported, will pass and that there is an option tailored and available for them.  This is especially true for students with Ds and Es in lower school.  For the first time, in Senior school these students have courses that are designed for them (Foundations and Essentials) and there is a clear path to find success.