Good thinking in deed!

The new South African cabinet really means business. The issue of one teacher training per province is long overdue. There is clearly a dire need for teacher training institutions that could be of NCS orientated.

We are struggling with learners who clearly are not having enough primary education. That calls for good groundwork at primary schools so as to maximize the possibility of learner achievement at secondary school level. I am not saying primary school teachers are not doing their best, but I mean to say we need to provide more support to these kids as the new curriculum is really demanding.

Hope we win!

Linking Personal and Formal Learning Theories

I find it very interesting that as educators we have our own believes on what works better in our classrooms. On the other, there are theories that suggest certain methodologies to best teach a certain or range of mathematical concepts.

The only challenge is for teachers to find formal learning theories that they can best subscribe to. I believe that would be one way to improve learning and teaching, especially in mathematics education.

Statistics Education

We have neglected a very powerful tool of decision making for too long in South Africa. I think the critics of the new curriculum can rest assured that Learning Outcome 4 is actually long overdue and we need to make sure that we can make it better.

The only challenge we face as teachers are the skills to teach this invaluable and indispensable branch of mathematics.

I wish we win as we managed the days of Calculus very well and today nothing can stop us!

Why teach math?

There are many skills that are taught in math. Take for an example a simple like to follow rules of the game. That is math! In these challenging times, math is an invaluable skill for each an every citizen. This makes it so important as the life itself. I wish that our kids will be able to appreciate the fact that "all is number". Without math there would be no future. Look at first world countries. They have invested in math skills for many years hence they benefit now.

Lastly, math teachers discipline, which is one thing we lack from the youth of today. I wish somebody out there can explain in the language that can be understood by these learners that math is the key!

Service Delivery debate

There has been a debate about the comments and views on service delivery from the DoE at kzncomp discussion list. The only worry I noticed from the two DoE officials who are actually hard workers themselves is the cover up of the person who din not discharge his/her responsibilities.

I think this is not a good practice, gone are the days when one person is lazy and incompetent, then we just keep quite and hire someone to cover up! People must get into position through merit!

My Math grade performance

I am proud of an average of 60% in the final assessment test for June, it looks like we are getting there with my young and honest honest ones. However, I noticed that they scored high on the sections we did last, which could be an easy assumption to say they have forgotten the other work.

The thing is, they are still young to study on their own, hence the fact that the DoE abolished Examinations at GET up to 8.

Was that a good idea? What do you think?

Common Testing at grade 11

Please let us be serious and take assessment as one fundamental aspect of learning and teaching. The papers that were written for both Math and MathLit were having a lot of errors in both question papers and MEMOs. This is clearly unacceptable.

These papers become public knowledge and there are learners who their parents are math teachers too and even worse DoE officials. How can we claim to have vision/mission of Quality Education if even assessment from Examination and Assessments Services is full careless mistakes?

I am sure, it is not that the people who set the papers are not capable, but Monitoring, Control and Moderation was not adhered too, hence a lot a errors manifest themselves across the entire question papers.

There is need to do things on time and careful monitoring. Cut unnecessary debates/meetings as they actually eat on work time. We need to make sure that we minimize talking and to work!
I am sure somebody somewhere is not doing his/her work properly. May be we need an independent Monitoring Commission just for Services and Implementation in the DoE.

Comments welcome!

Error on Math P2 gr 11

Math P2 common test had an error on sub-question 3.2. In the second denominator a cos (theta) was missing.

It shows the importance of moderating and checking of papers even at the stage of printing., as some mistakes can still be verified there and an ERRATA be sent to schools, that is common practice even at tertiary institutions. But if the paper is written and a memo is sent to schools already the damage has occurred.

Comments!

Archimedes said:

"Give me a place to stand, and I will move the earth." A very powerful statement indeed. To me this statement means, when given an opportunity, I will do wonders.

I like challenges and I believe all mathematicians enjoy challenges and in fact, that's what makes a mathematician.

Grade 11 Math P2 Common Test

This was really a good paper concsidering the range of aspects assessed. But still mark allocation is not what I can recommend for certain questions. However, good to see Trig (reduction formulae, definitions application) being assesed in that style. There is really an improvement or the paper was not set by the same person.

One error on numbering was noted, which was not a big issue, but we need to comment on errors so that examiners also lear as we are all students in this new curriculum.

Comments!

Locked in a box!

It looks like we have very few people who can share ideas in South Africa through taking advantage of available social networking tools and the power of the internet. I would like to communicate to as many math educators as possible, especially around South Africa, not just within my district or circuit, so as to validate the feedback/responses I get from my pupils that are they general or not.

I think we need to keep sharing ideas and communicating new methodologies to keep ourselves relevant and up to standard with the rest of the world. The use of advanced technological innovations like Twitter, Facebook, etc can be a very powerful tool for learning and teaching, not just gossiping!

I am really certain that, if we can even start by having things like discussion lists/group e-mails with the same interest in the Googlegroups or Yahoogroups, etc we can be able to get somewhere. Other subjects (CAT and IT) are taking advantage of this technologies, why not in Math, sciences, etc.

Comments!

Relating math to reality

It looks some of the topics we teach at school level do not make any sense to students. Take for an example Financial Mathematics. We introduce Bond/Loan repayment and some of the learners don't even know that you can have a house that is owned by the bank for 20 years or so.

The other examples, are that of inflation calcuations, nominal and real interest, tax calcucations hire purchase and measures of dispersions. These are specialist fields and even some of the teachers have to do a little research before they introduce some of these topics.

I am not saying these sections are not important, but I think the level of difficulty should be considered and we need to relate/give/illustrate sections that are unfamiliar to learners with careful considerations.

I wish that math be made as simple as possible so a not to confuse and demotivate students from the beginning. We are struggling to make math as funny and enjoyable as possible, but our students do not seem to enjoy it, hence they become so negative to math. We need to have some relevancy to their livelihood and keep them interested.

What does a 13-17 year-old want to know in math so as to keep going? This is the right quesion for curriculum developers and researchers.

We need to make math kids-friendly, not professors explorations - as that makes it too abstract, and kids do not identify with it and they just give up! May be we need to engage teachers more and more when it comes to curriculum content coverage and activities to use to accomplish whatever student envisaged by the curriculum.

Comments welcome!

Maths and Computers

I find it very interesting to solve mathematical problems through computer pragrams, that could take time on pen and paper. I think we need to consider the use of computers in math teaching as long as there is correct and appropriate like Graphmatica, Sketchpad, Mathematica, Autograph, etc.

I use Graphmatica (since there is freeware) often for checking on graphs.

There is a great potential in MS Excel if one knows how to use it with xy scatter for graphs. And there are lots of build in formulas for Statistics.

I think there is a need to consider computers just like we use calculators in math teaching.

Twitter in learning and teaching!

Are there benefits in using Twitter as one of communication means, since it is social networking tool that is gaining momentum all over the world, for learning and teaching in these challenging times? Schools in UK and US have tried this and they got mixed reactions as a result some of the schools have banned Twitter use.

We recently had a problem of MXit in South African Schools. The way Twitter works is a little advanced than Mxit. What do you think?

Follow up on Math P1 Common Test grade 11

I am not doubting the integrity of the persons who set the paper, s/he/they is/are at that level because of expertise clearly considered.

The concern I have is that of asking someone who does not understand the symbolism (and meaning attacked) used in math. One typographical error can mean something else in math. Take for an example and inequality sign replace with an equal sign in the equation:

(-x + 7)(x + 5) <=0 , the solution here will be x<=-5 or x>=7.
But if there is an = sign only, the solution is totally distinct,
the solution becomes x = -5 or x = 7.

At the same time we need to note that if we had a division as (-x + 7)/(x + 5) <=0 the proviso will be required; as x cannot be equal to -5. That is why math is very strict with symbols!

I think all mathematicians/scientists must learn to type their math/science question papers and memos. That will minimize unnecessary arguments and debates. We need to get to real business of fighting the problem of math performance in our schools, not fighting clerks that take incorrect math or erroneous papers and memos. After all, we all do mistakes when we type, but unfortunately math does not like mistakes. It is a very strict subject, hence we need to blame the mathematician for incorrect math, not the typist or clerk!

Comments welcome!

Common Tests papers should be thoroughly moderated

Noting the mistakes found at grade 11 common papers, there is a need to start to be serious about assessment.

I would like to stress the fact that a common test for mathematics must be thoroughly moderated. It is really embarrassing to see mistakes on both the question paper and the memo.

Examination and Assessment Services and Curriculum should take this as challenge and need to address it before it is too late.

Comments welcome

My experience on Math Lit tutoring

I have enjoyed this activity for almost 2 years , as I started in 2008. The interesting thing is that of finding that, there is not much of a big difference between teaching the young ones and the grown ups (adults). The challenging thing is to get the adults to be on task and keep them working.

The other difficulty is that of finding more able few individuals that can get along with all tasks without your assistance and while you also get those that need to be taken step by step to reach a reasonable and acceptable level of performance.

There are challenges, since these are working parents with families to look after and at the same time they have to do assignments/tasks and study for tests and examinations. It is not an easy thing to manage, but others are disciplined enough, hence they get along with tasks and be able to participate in discussions and so on.

The experience I gained here is a wonderful one and I am learning a lot out of Mathematical Literacy and looking forward to the controversial modules of Teaching and Learning and Professional Practice in Mathematical Literacy.

I like the University of KwaZulu-Natal approach to the ACE programme as I believe that some theoretical understanding on Math teaching is of fundamental importance, so as to realize and be able to respond correctly to challenges in class during math lit teaching and learning. This is a must, especially for the Math Lit learners.

Comments welcome!

Very difficult times for math teachers

It looks something is lacking at primary schools math teaching and learning. I wonder if grade 7 classes are really being taken care of so as to prepare them for grade 8 and 9 math AS. The way our curriculum is structured, it is such that a learner progresses from grade to grade with content coverage.

Since I have had the opportunity to teach grade 8 in two different schools for in the past 5 months, I have noticed common errors in math concepts that are supposed to have been mastered or at least to a certain degree. Take for an example, fractional concept. This is one problematic and often misunderstood concept. At grade 7, recognition of simple equivalence which is very important for further fractional conceptualization. Then at grade 8, formalization and operations takes effect. At grade 9, some common fraction are used with complex but comprehensible operations.


This is one area of concern out many. I think may be some communication with primary schools is a necessity.


Comments welcome.

Mathematics P1 grade 11 June 2009 Common Test

It looks like NO moderation of the paper took place if one looks at sub-question 1.1.4 and 1.4. The mark allocation for 1.1.4 is 6 marks, for something that can be solved by inspection since 12/x+5 =1 implies that x =7 without any calculations. I am really concerned about the fact that this was a huge discrepancy on mark allocation. How can this be 6 marks?

With regard to 1.4, it should have been mentioned that "without using a calculator" as some calculators can take more than 10 digits keying in. I wish to bring to the attention of current and future examiners that researching and investigating various approaches to answering questions is of paramount importance for the best formal assessment in common testing.

Comments welcome!

Common Testing at grade 11

This was a very good initiative and I believe that we have benefited as educators and needless to say the learners are really finding this external examination in a common testing fashion very useful to prepare them for grade 12.

The only thing that has destroyed it altogether, is the management of examination papers. The are schools that write these papers at their convenient dates. That obviously nullifies the whole exercise. I don't think they serve any purpose for the schools where learners have had access to the examination paper and then write the same paper for formal assessment purposes.

There is a need for the DoE to review the channel of communicating the papers to schools and apply strict control if really we still need to benefit out of this exercise. Otherwise, other options must be explored. For an example, the use of technology. We need to go with times! These papers can be available on line on password protected fashion that is per school. Once the school has downloaded the paper, there should a record of date and time. Then there will be a tracking system to check who had the paper downloaded on the unauthorised date/time. There are lots of opportunities that were can explore. They are also very cost efficient as well. We just need to have the right mind and will to change.

Comments welcome!

Trig issues: Radians vs Degrees

We decided to effect some changes in the math curriculum w. r. t. Trigonometry for the new curriculum for some reasons. One of the changes is that of the inverse ratios that are no longer being taught at school level. The other one is that of all identities that include inverses that they are no longer in the school curriculum. I taught those were informed decisions when I first looked at the NCS, but now I am totally against those changes and wish they were retained.

The development that I thought would have been introduced at school level is that of radian measurement compared to degrees. This will better explain the issues of accuracy when it comes to practical problem solving in trigonometry.

We need to make changes for better understanding of our sciences and applies sciences, not just for the sakes of changes.

I am really concerned and wish that our math curriculum be reviewed, not unless if someone can fully convince me as I believe what I have read in the NCS does not convince me.

Why teach Mathematical Literacy?

This is one very difficult question as there are several and conflicting views nationally and internationally on what it really means to be mathematically literate. From the South African schools perspective, Math Lit is taken as an inferior math that should be taken by those who are not that capable of doing pure/core math. This is an unconscious view prevalent in most schools and even departmental officials.

The truth is, this is not an easy math, but an alternative math approach. If one looks at the LO's and AS's in NCS, it is evident that this just another mathematics equally difficult and at the same level of academic and citizen expectations, just like the one doing core math.

I therefore believe that a paradigm shift is needed to both learners and educators (DoE officials included) so as not to take math lit as a mediocre subject for the under perfomers. By continuing to undermine this invlauabe subject, we would actually be underining the greatest initiative taken by the South African government to prepare numerically, finacially, spacially and financially responsible citizens.

I think debate and awareness on what is the envisaged learner and future citizen should be the direction of debate, not to just push to math or math lit without careful guidance from grade 10. Career guidance should be a way to go so as not to dump or force in or out learners into math lit.

We need to debate this further, hence your comments are welcomed!

A video clip to catch Schools Confed mood

My School won the Msunduzi Schools Confederations Cup

Following the hard work of both learners and the teachers, Siqongweni High School managed t o be number one out eight schools that were participating in the Msunduzi Hgih Schools Confederations Cup, where Siqongweni was representing the country USA.

This was a great achievement as three boys are now tipped for the top Premier League teams. One of the boys is the schools goal keeper who won R3500 for being the best player of the tournament.

There were dignitaries like Mike "Sporo" Mangena, in these tournaments, hence it was easy for the boys to be recognized and connected.

Thanks goes to Msunduzi Municipal Deputy Mayor, Mr Zwe Hulane for the well organized tournament with good prizes. Siqonweni received a first ever Schools Confederations trophy, R15 000 for winning the tournament, and R3500 for the best presentation category out of 8 schools.

Mathematics Grade 11 Investigation Task

Mathematics                                           Grade 11                                           Investigation Task

Due date: 16 April 2009

 

N.B. This task will form part of your portfolio assessed using the attaché Rubric.

Successive Approximation Algorithm

Successive approximation is an iterative algorithm for approximating the square root of a number. The algorithm is based on the following observations:

If x is the square root of N then,
(1)    (N/x) = x so
(2)    (x + (N/x)) / 2 = x.

It can be shown that if y is an approximation of the square root of N then,
(3)    (y + (N/y)) / 2 is a better approximation.

Using equation (3) repeatedly allows an approximation for the square root of N to be continuously refined. The refinement of the approximation may be stopped once the difference between successive approximations is less than some threshold.

 

Math error!

Most (if not all) calculators give the output of division by zero as "error" or "math error." This is really misleading to our learners and distorting the concepts of the meaning of division by zero. I am really against this programming of calculators and wish that the correct term, "undefined", should be used.

I am suggesting this because to date there are programmable and graphic calculators these days, hence we need to make sure that we stick to correct mathematical terms. We have enough problems in our math teaching, I think programmers/companies of pocket calculators need not to make our too difficult more while they think they are making it better with calculators.

Your comments are highly acceptable.

The Principal and his successful former students

Mr Mpulo principal of Siqongweni, was delighted to see Mr Zwe Hulane, now deputy mayor of Msunduzi Municipality and Brian Zuma (former P4 DJ and now PRO of Municipality).

Siqongweni represents US style for School CAF

This was a mini presentation organised by Msunduzi Municipality where an USA soccer squad jersey was presented for the Soqongweni soccer Team to use during 5-6 May School CAF.

Guests of honor were: Doctor Khumalo, Mike Mangena, Zwe Hulane and dignitories from MTN and Msunduzi Municipality. Below are some of the photos taken during presentation.

Negative angle measurement in CAST diagram

I use an easy(for my learners) method that makes sense to understand the negative and positive angles in CAST diagram. The method works like this, if you are given a trig ratio sin (-225). Take 360-225 = 135. That means sin (-225) = sin 135. It sounds logical as the revolution (by convention) is 360 degrees, hence an anticlockwise + clockwise measure = 360 degrees, as two such angles share a co-terminal, which is actually one and the same position in terms of CAST diagram.


I was very pleased to let my learners get an easy approach to this abstract concepts especially with limited technology.

I wish I could comment on this.

We are not alone in Math battle with students

I have been trying to get some views from other countries and realized that we are not alone in this battle. US has serious issues ranging from learner discipline at school and no help at home, sounds South African, for sure. As a result I came across some initiatives from the link below:
http://www.idra.org/Services/Math_Smart!_Secondary_Training/

Just to refer to what they aim to achieve among other things is:

• Implementing the five dimensions of mathematical proficiency in a standards-based curriculum.
• Using cognitively guided instruction: Questioning techniques, teacher strategies, and building the classroom environment.
• Ongoing assessments of instructional efforts.
• Differentiating instruction in the mathematics classroom.
• Developing literacy skills (writing, reading, and building language in mathematics).
• Implementing cognitively challenging standards aligned strategies for student success in math.
• Supporting teachers through mentoring and coaching strategies.

I really found the above quite informative and would like to get some comments from whoever is willing to change math perspective in Southern Africa.

I am sure We can!

LO 3 for grade 8

I was trying to introduce transformations to my math class and only top find that most(if not all) of them could not associate Points, lines, line segments and angles, hence I had to start by introducing that first. I believe that, not knowing enough of learners content coverage from grade 7, makes it quite challenging to keep up to the standard what is supposed to be taught at grade 8 as per SAG. I wish there should be a way to guide and monitor grade 7 teachers as well. That would help to limit surprises at grade 8 and onwards.

But I will not give up with Transformations, I will actually come back to it in due course.

Hope to here year comments.

Transformations at math grade 8

I have noticed that grid papers play a critical role for the learners to grasp the concept of transformation at early stages before it gets to abstract. I plan to use some pictures dram in a grid paper/dot paper so as to carefully show that there is some sense in common axes and thus be able even to introduce formalization of concepts like reflection, translation and rotation. I believe that all of as math teachers should start to see value in groundwork before introducing abstract concepts.

Parts of the circle lesson @ 8

I was trying to introduce my math grade 8 class on the LO of Space and Shape towards Transformations. I think this is one section quite critical and determines future in maths at FET level. I really enjoyed it. I wish to provide a video as it progresses, so as to share it with others.

One of the days

I think today was one of the days that I had more hassle then successes, after having finished my grade 11 short test marking, it came up that there are still some misconception on special angles and the reduction formula in trigonometry. I therefore would like to thoroughly revise this section as I believe that it is possible to master it at grade 11 level so as to make sure that they don't battle with more intricacies at grade 12 level.

I enjoy the challenges I am facing, it's like I am teaching for the first time as the learners here are not that very disciplined and dedicated. But I am determined to overcome all barriers and at least get the majority to grasp maths and be successful in future studies.

Hope to hear your comments.

Math problem solving at grade 8

Today I gave my grade 8 class a problem solving question (again), still there are struggling. The problem is: Magda spent 2/3 of her pocket money on sweets. If she spent 54c, how much did she have?

I was really shocked and I had to use R3, 30c, etc. They were then able to figure out the trick taking 54c divide by 2 and be able to get 27c and conclude that, Magda had 81c.

This is one challenge still about the language usage in mathematics. I really believe that there is something missing out in our math teaching, hence the poor results in most areas.

I am one of the people who believe in doing something, that is why I would like to take a challenge of trying language related problems with my class so as to convince a reasonable skeptic that language does matter.

Hope hear your comments.