South African Math crisis!

It looks like the dismal performance of our matriculants this year testifies to the fact that we are in trouble! I noted this long time ago in this blog and now we are facing the challenge as a reality.

I think there is a need for an INDABA on math challenge as the problem is not only with the examination, but also with the teaching of mathematics at all levels within the South African new schooling system, OBE. The National Curriculum Statements are very clear and also good. The problem lies with the content coverage where textbooks jump from one topic to the next with necessarily giving learners enough content engaging.

There is really a good pool of resources that we can take advantage of, all we need is a clear directive from the math education experts and start now to improve learner performance.

Comments....

Grade 12 Maths Examination 2009

The papers were rather challenging, even though the standard was OK. I think there is a need for creating a bank of questions by the examiners so as to make sure that educators are not textbook bound. The thing is, there is very little data to prepare learners towards good examination questions.

Mathematics is one subject discipline where the scope of questioning is unlimited, as a result with a new curriculum, it makes it very difficult to cover as most question dynamics as possible as you can.

I think the new curriculum is good and all it needs is support and continuous learning and development from the side of the educators and DoE in general.

Comments...

Revision w ith grade 11!

I have been preparing my math grade 11 for up coming final exams, was really surprised that they have forgotten some basic stuffs on algebra, trig and so on. This is actually discouraging as I had to reteach some concepts and then they remembered.

I am a bit worried about the state of learner memorization and commitment to learning in general. It looks like most of the students just come to school and think that, that makes you to know/learn. That is actually not true as learning a lot of your self reflection on you can or cannot do or remember.

We are really struggling as teachers, may it's about time we consider modular based training, where learners are tested on sections/modules content covered and then move on to the next level.

Comments....

Mensuration section at grade 11

This is a rather simple section if learners have a necessary foundation towards exploring complicated shapes of problems involving Surface Area and Volume. I encountered a huge challenge with my grade 11 today as they seem to have not taken this section seriously from lower grades, now they can't even remember the rectangle, square areas formula. Anyway I tried some basic shapes to make sure that they remember triangle formula as well.

It was really a stumbling block for me to continue to grade 11 complicated sections, however I will persuade them and see to it that they grasp necessary information on this section as it prepares them for careers in quantity surveying and the like.

Comments...

Problem areas with calculator usage!

I find it very difficult to explain generally to the whole class on what keys to press when doing some calculations based on functional keys like cube root, index/powers, and even trig ratios or so. The problem is that calculator are designed and programmed by different companies as a result their functional of logic/programming is not the same. I have to first check on what calculator the student is using an then explain relevantly to the order of the logic it follows. Really confusing for some students as they sometimes share or borrow different calculators at a time.

Comments....

Graphs in grade 8!

I started general graphs with my math grade 8, they liked the idea of using grids just to get into familiar with the use of co-ordinate systems. The interesting part is that, I took this as a simple exercise, but was a little bit challenging to others. I used numbers for both axes so as not to confuse them when I introduce the Cartesian plane. It worked very well, they are Ok with the terminology of x-axis and y-axis, however some of them still struggle with which number to belongs to x and which one for y.

I will now introduce the negative part of the Cartesian plane.

Is this a good idea?

Comments .............

Today was one of my best days at Maths Lit

Teachers were engaged in Research Report Writing, and they had to then reflect on their professional development/growth. They are going to do some self/peer assessment on their Reports and also do Short Oral Presentations on Fridays.

Tomorrow it's only Teaching and Learning. They will be writing an open book test based on contexts that were given weeks ago. They were also asked to bring curriculum documents to refer to certain aspects of the test.

I wish all teachers should do some professional development! This is a great course indeed!

Comments welcome...

ACE Mathemarical Literacy

As a tutor for the in-service teacher training for math lit, I really do benefit a lot and would like to explore some of the ideas in my own math teaching as a professional. I have been explaining some critical aspects of a good action research report to student teachers. They really are getting it well.

The interesting part, was the ideas on mathematical proficiencies (strands) by Kilpatrick.

These proficiencies are really excellent!

Comments,...please

Power of Box and Whisker plots

I gave my grade 11 a short test, as a tradition for every Friday. I was a bit curious to show them the applicability of Box and Whisker in real data set, since we did Data handling some time ago, but the test was on trig formulas. I therefore quickly marked their scripts!

I came back to class to give them back their papers. They were so happy to get a quick feedback. However, they did not realize that there was motive behind giving them their papers.

I quickly wrote the scores on the board, most of them realized that, these were their marks. I then asked them to work with me in arranging the scores in ascending order. They were very enthusiastic! I asked them to give out the Five number summary, they did it with a lot of accuracy and attention. I then asked to watch me drawing the Box and Whisker plot on the board.

I became evident that the students who had their marks in the first quarter are the typical culprits, often called for discipline problems and usually abscond or absent themselves. They really appreciated the power of Box and Whisker plots and wanted to ask more questions about its validity and reliability.

I was so amazed with the participation and wish I could find more to do with the Data handling real application that makes sense to students.

Comments welcome....

Calculator difficult than a Cellphone

Today I tried to do a little bit of survey to find out how students of these days perceive calculators compared to cellphones.

It became evident that they struggle a lot with a calculator, while they quickly master the cellphone feautures quicker and better.

I therefore think that, the best way to teach the calculator skills is through giving students an opportunity to explore on their own with the capabilities of the calculator. I wish to try this out and see if they can master the calculator to best potential possible.

Comments welcome.....

Maths is really challenging without a background

I have been introducing my grade 11 to Sine Formula and its application in triangles. Some of the learners have forgotten the fact that the sum of angles of a triangle is 180 degrees, I quickly had to set up an activity on revising this for 10 minutes. It really was blocking me to continue. As if that was not enough, some students could not find the angle if given one angle and two sides, they have forgotten the use of second/inverse function/ratios in trig equations. I also had to prepare a quick revision of that on the board to remind them on how to solve such problems.

Really maths is demanding, especially with these forgetful students of today.

Comments welcome...

Perimeter of a Circle at grade 8

This is a complex concept in math at early stages like grade 8 (12-13 year-old), however I managed to introduce it so nicely with a cut paper. I took 40 mm as the radius and asked the learners to draw a circle using the pair of compasses. They managed to draw it without any problems. I then asked them to try and measure the length of the circumference. They really struggled and I came in to assist with a cut piece of paper.

They had to measure the arc of one side and then multiply by two. They were so happy to see that it is actually possible. But I said, you know with math we need some generalizations and formulas, hence I introduced them to the idea of C = pi multiply by diameter.

They were amazed! I think hands on experience in mathematics makes sense to the young minds. I would appreciate comments.

Math and Stats

Today I noticed that my learners can easily most calculations in stats, but when it comes to interpretations they really struggle.

I think there is is thin line between math and stats. As teachers we need to take note of that our learners struggle with making sense of numbers or values calculated.

Measures of Spread...Statistics

I was trying to explain to my learners that, the number of data sets (scores) can be a sample or the actual population. It was a rather worse when I said that, when the data is less than 30, you need to divide by n - 1, not just n. They were confused. I think this is a very powerful statistical method that is beyond grade 11 comprehension. I think we rather stick to one formula. The catch is, we have to incorporate both scenarios as it depends on the data given.

On a more positive note, they managed to master the three spreads, i.e. variance, standard deviation and mean deviation. But they need more examples to see how to make good interpretations of the results. I really enjoyed this session.

Comments welcome...

Cumulative frequency Graph or Ogive

My learners were so amazed with the power of Statistics when it comes to graphs. They were seeing/getting explanation of this graph for the first time and they appreciated the ingenuity of statisticians.

This came up as a result of them being involved in a research project, where I was trying to do statistics in a practical way. This is one way to encourage learner participation.

Teaching Math is demanding

I have noticed that some of the important issues are ignored in math education. It is high time that we consider math as a human right as early as Grade 0 or Year 0 in the formal schooling education.

You find that a lady in elementary education/primary has very little mathematical thinking herself and she is taken to teaching math at lower classes as if it is an unimportant, easy math. This is wrong impression as if the child is not exposed to good and correct number/numeracy understand at relevant point in time, the chances of being successful in math are so slim.

I therefore believe that specialist math educators/teachers should be a way to go at all levels of math education to be successful in future.

Today my math grade 11

I really enjoyed showing my learners that, even though their performance was not very good in the June Examinations, they were happy to see that I take care of them. It looks like as educators we need to keep on encouraging these learners that they can make it. Telling them that it is "YES WE CAN."

I think my learners are a bit disadvantaged as they don't have many successful educated people within their families. It is really hard to explain and encourage young minds. Teachers are doing a great job out there.

Reading and understanding in Mathematics

After having analysed all grade 11 maths results for the June 2009 papers, it became evident that, learners are not equipped with enough skills to read and comprehend the questions. This is prevalent in the questions where, for an example, the question says no use of a calcucator, but you find numbers/solutions that clear come from calculator.

Some of the students could not relate sections accordingly as a result they ended up appyling an incorrect formula, e.g. trying to use Quadratic formula to solve a linear equation.

I think, some emphasis on understanding what the question really wants is of paramount importance, hence I have decided to start the paper all over again and explain the concepts relevant in each question. It is a mammoth task, but what can I do with learners already in grade 11, but cannot read with comprehension.


Comments....

Mandela and numbers

First it had been 46664 used for HIV and AIDS awareness, now 67 minutes for the social activity once a year. These are interesting numbers as they arre not just numbers, but mathematically important numbers.

The first one, 46664 is a palindromic, and now 67 is a prime number in the form 2^6 +1. The other obesrvation is that 6 + 7 = 13, which is also a prime. These are interesting observations to me as a mathematician.

I am trying to look at how math and mandela are related.

Comments welcome...

Mathematical Literacy challenges!

There are quite a few teachers who are challenged in understanding the nature of math lit. I therefore believe that it is important to keep training as many teachers as possible for this subject to be succeccful.

I have lectured/tutored the same group three semesters and note that there are gaps in some aspects for certain students. There is hope as they have improved a lot from the date I started with them a year and a half ago.

We have done interesting hand on activities of which I will upload pictures in due course.

Our math is going down!

It looks like our learners are going down when it comes to math skills. I have noticed this in the June 2009 results in my school and compared it with some of the teachers I met. The learners of today are taken care of through a number ways, but still are not making it to their full potential. I think we need a national and international compaign with regard to math educatuion. There must be initiatives all over to see to it that students are taking math seriously.

Math is an invaluable skill. We need to take this challenge very seriously as math is one subject that instills discipline in education and learning in general.

Comments welcome!

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.

Integration of ICT and Maths/Sciences

I am one of the people believe that technology/computers, sciences and mathematics is the future of all developing countries.

The initiatives like Sciences Expos, Investors, etc are a way to go and need to be nurtured to all learners. I therefore wish that there should be more and more of these activities/project competitions.

The only challenge is to get enough good participants so as to keep the standard as high as possible. I also think that, since there are more primary and secondary/high school participants coming up, may be there is a need to consider taking primary schools and secondary/high schools on separate days, but following each other.

I am sure may be that's one concern you had considering the numbers this year.

Hope to hear your comments. Well done, again!

Integration of ICT an

Siqongweni also participated at Olwazini Science Expo

These were so passionate learners that have just joined the school at grade 8, but they can do Volcaneo and Water Purification projects. I was really impressed!

Olwazini Young Scientists Expo

Today I was involved in judging at the Eskom Young Scientists Expo held at Olwazini.

I was really impressed with the learners work. I wish more and more of these opportunities could be created to encourage project-based learning. There were about 150 learners representing different schools from Primary level to Secondary level. I wish to extend a word of appreciation to Olwazini staff. You did a great job, keep it up and continue to create these opportunities for our kids. We are really proud of you and,

TOGETHER WE CAN DO MORE!

Grade 11 Trig Revision

I have to prepare my learners for June Examination. They are actually struggling with Trig. I am going to try and give them more practice exercises. I have noticed that, there are some misconceptions that I have to iron out before they write Mid-year Exams.

It is really challenging to teach math if learners are not that fully developed in thinking skills, hence I am trying to inittiate problem-solving at grade 8 level from this year.

Teacher Laptop Initiative

This is a great move from the DoE and in fact something like this is long overdue. The challenge will be to make sure that there is fair distribution from the start, so as to avoid one-sided development while ignoring one large portion. I think there should be a clear model to be followed so as to make sure that educators get equitable fair chance to access this scheme.

One challenge obviously will be to monitor the whole project. I think capacity has to be build at district/circuit level. There is a need to carefully monitor that there is no abuse of this scheme as some educators can take chances. The Government Gazette (8 May 2009, No 32207) speaks to some of these issues, but the thing is, that is just a document like any other government documents. There is need for proper and careful monitoring, otherwise we will wake up when it is already late.

On a positive note, the Gazette has specifications on hardware and software. I have a concern with the battery power of 2 hours. The school day is maximum of 7 hours. Some laptops batteries can go up to 3 hours. Again these are just estimates depending on the processing of information, same like cellphones (depending on calls). I therefore suggest a special concession of a spare battery in case the educator is in a school without electricity. This is one area that needs to be looked at. Another one is that of printing. There must be a move towards considering providing network printers to schools. Another challenge if there is not electricity!

I have just highlighted a few issues, there are actually many, but I give the project a thumbs up!

Grade 8 Math problems

One of the days, I gave my grade 8 a language related math problem. It became evident that there were struggling and I opted for vernacular, they understood and then they were able to solve the problem. Language is really an issue when it comes to problem solving. I wish somebody out there can make our educationist/curriculum developers make it a point this matter is addressed before it's too late.

The problem was "The sum of the two numbers is 2 1/4 and one of the numbers is 1 2/7. Find the other number." They were struggling and some of them added these numbers since they know that sum has to do with addition. I was really concerned as this is basic arithmetic having to do with language. I wish we can do justice to our learners before the damage is too big and unbrearable at grade 12 level, where everybody seem to whoo-ha!

A Typical Math curriculum problem

In Trigonometry, inverse ratios are not longer covered according to NCS at FET level. This was one of the decisions that made mathematics to be a little bit below standard. I have been trying to solve the problem given last in June, 2008 P2, grade 11, trig problem was, if tan 25 = a, determine, in terms of a: (tan 205 - tan 115)/(tan 245 + tan 335). It became too cumbersome to evaluate this without using cotangent and 270. I am not sure if enough research was done so as to remove this powerful reciprocals knowledge.

But, I think we need to get used to living into the future and not complain too much. Math is hear to stay and curriculum can change with mankind needs and requirements.

Worldwide event in Hong Kong, Nov 2008

When I was in Hong Kong! This was the worldwide event for Microsoft Innovative Teachers

Not entered ITA 2009

This year I did not enter the Microsoft Innovative Teachers Awards. The thing is, it was too early for me as I am in a new school with very limited ICT resources.

I am looking forward to hear and see that good projects were idenitfied and won.

Good luck to everybody!

My grade 11 Math Class

Today, I really felt so embarassed to find morning clasees math learners waiting for me for almost 30 min as I was late. I started by taking my wife to her new school. I was not aware that traffic can delay me so much. Learners understood.

On a positive note, they really enjoyed my shortened lesson as I gave some tips on Reduction formulae, Special aangles and the use of CAST diagram without using a calculator.

In the other group of grade 11, the lesson was more of tips and strategies on how to best apply reduction formulae. I really enjoyed my two math lessons and it looks like my bad start of the day made me to think hard and fast, so as to best teach, may be one needs to be continiously challenged to keep going.

My career challenges

I've noticed of late that I'm actually on the verge of becoming one of the critics to my job. This came as a result of noting that very few learners can do basic mathematics even at grade 11 already. I think, as teachers, we need to check whether we are still relevant or coping with the new gerataion way of thinking and learning. I don't think that these learners can't do mathematics, may be it's the way we teach them that is boring and not interesting to them.

I wish to undertake a study on how best to meet the standard of these learners so as to teach them in a way that can keep them interested and willing to do more and more learning. My take is, Information and Communication Technologies is one way to try and keep these learners interested. We need to find a way to use mobile phones and video games so as to keep them interested and appreciate the value of education even in these gargets that they are so fond of!

Maths teaching

Today I noticed that my learners are not actually doing enough work independenty. As a result they seem to forget easily. I spoke to them very strong about the dangers of relying on one person to the work and let others copy. They seemed to understand my concerns and I have to keep an eye if they keep the promise. It's really hard to keep them learning as they think that as a teacher I have to tell them everything.

Twittering

I have really considered Twitter as one of the powerful technolgical tools than can be taken advantage of in teaching and learning. I am busy exploring ways and means that one can benefir from this mobile and PC blogging compatibility. If you have any ideas please feel free to comment on my blog.

Thinking about making myself visible

I hope sometimes an individual misses to be visible. I say this because I can see that I have great ideas but not having much opportunity to share, hence I decided to start this blog. I hope my voice will be heard. All I need is to invite as many followers as possible. I am also involved in Twitter!

School to School migration

After leaving Mpophomen High School on the 5 September 2008, I managed to land myself on a number of challenges, but I survived.

I was then place on the 18 February 2009 at Injoloba High Schoo. I was responsible for teaching Mathematics and Technology grade 8. It really enjoyed working in a new environment. My highlight in this school was when I applied for the school to be taken for the one year free internet organised by e-Schools network. The school qualified according to requrements set.

After all processes of my placement were followed, I was then temporary placed to another school, Siqongweni High School in IMBALI township on 18 March 2009.

I really enjoy the new challenges I am facing in this schol and looking forward to shine as I did at Mpophomeni High School.

About Thami

Born in a rural area called Mpumuza (Pietermaritzburg-South Africa), a son of Alosia Makhathini and David Vela Basi.. Attended my primary education at Bkekizizwe Combined school from 1980-1987. Thereafter from 1988 to 1990, did my secondary education at Insika Secondary School. In 1991 moved to Umsinga as there was high level of violence in KwaMpumuza. My mother decided that I go to do my high school at Somashi for standard 9 and 10.

I passed my grade 12 with B in Mathematics. In 1993, registered at Indumiso College of Education for Secondary Teachers Diploma (Technical), where my major subjects were Mathematics and Motor Trade Theory. Finished my Diploma in 1995 and passed Mathematics and Mathematics Didactics with distinctions.

In 1996, I went to Umsinga-Greytown area to work there. I was employed as Mathematics educator for grades 8-12. I also taught Economics as there was no teacher for almost a year in grade 11. One of my best students got A in Mathemtics and I was very proud of that.

In 1997, I continued with my studies on a part time basis at Natal College of Education. I was doing Further Diploma in Education (Computer Literary). I passed the diploma in 1999 with distinction in Compuer practicals. In the year 2000, I was promoted to become the Head of Department at Busana High School still around Grytown. I introduced Computer Studies as an examinable subject at grade 10 and continued up to grade 12. In 2002, there were 12 students that registered externation examination for Computer studies and they all passed it. I was vey proud and entthusisstic with ICT at that stage. I connected myself with Hilton college in 2002 and thrrough the Vula Pragramme managed to get involved in a lot of Computer training courses.

While the above challenges were on, in the year 2000, I registered for Bachelor of Education (Leadership in Mathematics and Science Edcuation) through the University of Natal. I did this honours degree on a part-time basis and it was very difficult as some of the assignments were to be typed and submitted on line. Since then, I realised the power of the Internet and never stopped using it and now one of the gurus in internet computing.

In 2004, I was moved to a school in Dalton where my expertise were needed, but circumstances made me to look for a post in or around Pietermaritzburg. I got the post in Howick at Mpophomeni High School, still as a head of department. The interesting thing is that, I was actully on the verge of completing my Masters degree, but did not as there were challenges with my focus of the thesis. I managed to get directed in the year 2006.

In 2007, I was nominated and won the Aggrey Klaaste Mathematics, Science and Technology Educator of the Year. I won a 20 computers from Telkom Foundation and Sowetan. These computers were installed and networked at the school. I felt honored to recieve such a price for the poor community at Mpophomeni Township. This award was at KwaZulu-Natal Provincial level and hence I qualified to represent the province at the national level. I was thrilled to here that I also won at a highly contested level where all provinces were resperesented. The panel of experts there was educational practioners from schools, colleges, universities and even government representatives. I won the Further Edcuation and Training category and received a price of science kits for the school laboratory. I also granted the life time membership of the Association for Mathematics Edcuators of South Africa (AMESA). This was the great year as I manged to complete my masters in Mathematics education with distinction in my thesis.

The above accolades opened doors for me to nationally interviewed at SAFm and covered by the press at local and national newspapers. I was overwherlmed with the support and appreciation of the work from the friends and family, especially my wife Zandi Makhathini. She was the main sourse of inspiration to all my achievements. Not forgetting the support and encouragement I recieved from Pietermaritzburg Maths and Science Teachers Association (PIMSTA). This association has developed me professionally and educationally. As a result I am now holding an executinve position at national body Association for Science Educators of South Africa. The possition I hold there is that of a Public Realtions Officer (PRO).