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RTE 2 FM countdown 606 ( leaving cert program)
Rte 2 FM countdown 606 leaving cert program will be answering your questions on maths and in particular project maths. Please email your questions to countdown@rte.ie
John Brennan will be answering your questions.
UCC maths department report very critical of Project Maths
UCC maths department very critical of Project Maths
An eminent group of mathematicians based in University College Cork consisting Professor Emeritus P. D. Barry, Dr James Grannell, Dr Finbarr Holland, Dr. Donal Hurley and Dr Michael Cronin, have produced an Interim report on Project maths in November 2011 .
In a summary of their findings they say that they are deeply concerned about the following aspects of Project Maths.
(i)The exaggerated claims being made for the new approach.
(ii)The overwhelming emphasis being placed on real life context for study, and some examples which have already been developed for this purpose.
(iii)The inadequate preparation of teachers who are expected to teach the new syllabus.
(iv)The unnecessary haste which the new programmme is being introduced into schools, coupled with delays in providing syllabus details which is causing confusion and anxiety among teachers and students.
(v)The scarcity of suitable textbooks covering the proposed syllabus.
(vi)The choice of material being dropped from the older syllabus.
(vii)They are also very concerned about the influence of the PISA philosophy of mathematical education.
Full report can be found at : http://www.ucc.ie/en/euclid/projectmaths/ProjectMathsInterimReport_Nov2011.pdf
Project maths Statistics some clarifications
Questions and answers On Statistics:
The NCCA very kindly answered the following questions on statistics.
Question Can students be asked to find the median from a frequency table if the class intervals are unequal?
Answer Yes, if suitably scaffolded.
Question Is the 95% confidence interval on or off the course?
Answer Yes!
Question Can students be expected to use (95% confidence interval) Answer No
Question: Can the 5% significance level be examined? Answer Yes
Question: Can the words 95% confidence interval be included in an exam question?
Answer Yes.
Question Can the words 5% level of significance be included in an exam question?
Answer Yes
Question: What margin of error is used?
Answer: The hypothesis test that is examinable uses the margin of error for a population proportion (1 divided by the square root of n) as set out in the syllabus, i.e. effectively a confidence interval.
Question: For the margin of error for a population proportion are students expected to know where comes from or justify the formula?
Answer: No, they are not expected to justify the formula. They should appreciate that this margin of error (approximation) gives what is effectively a (95%) confidence interval for the population proportion based on a sampled proportion.
Question What is the NCCA definition of margin of error?
Answer: The margin of error referred to here is the maximum value of the radius of the 95% confidence interval. This will be included in the syllabus (Strands 1-5) to be issued to schools this summer, for first examination in 2014.
Question: For hypothesis testing what are the essentials?
Answer: In conducting a hypothesis test, the student is expected to identify the null and alternative hypotheses.
Question Is the Central Limit theorem on the course? To answer the SEC Q7c 2012 Sample knowledge of the central limit theorem was required. .
Answer: Formal treatment of the Central Limit Theorem is not required. As a result of their learning under Section 1.3, students should be able to construct sampling distributions (and see that they are approximately normal distributions) and so describe typical features of these from their exploration using simulations.
Question: How under exam conditions will students be able to construct sample distributions? To see that the distributions were normal would require many samples? Is this just an exercise for the classroom? It is very difficult to see how students would have time to construct sample distributions in an exam.
Answer: The particular question required knowledge from their classroom explorations/simulations. They are not expected to perform the simulations or construct the distributions at exam time. As indicated in my earlier reply, they are required to describe the features of the distribution in this case, not construct it.
Question In your opinion can this section be taught without reference to the central limit theorem?
Answer: Yes, I think it is possible to carry out the class activities so that students can get an understanding of such sampling distributions without formal treatment of the CLT.
Question: With regard to the empirical rule are students expected to know all 3 cases (68%, 95%, 99%)?
Answer: Yes, but 95% is the one most typically used.
Question :I note there is a change in the section 1.5 in the 2012 it stated “recognise the importance of representativeness so as to avoid biased samples” In 2013 “recognise the importance of randomisation and the role of the control group “ Can you clarify what are the significant differences?
Answer: The learning outcomes at FL and HL were interchanged for the 2013 syllabus, since the committee viewed the ‘randomisation…control group’ outcome to be a more complex concept than the ‘avoid biased samples’ one.
Other questions: Geometry if a students uses vectors to calculate the centroid of a triangle is this acceptable?
Answer: Yes, any valid method may be used, unless otherwise specified in the question.
Mean,Standard Deviation ,Correlation coefficient, and regession line from sharp and Casio Calculators
The following give the methods for finding mean,standard deviation and correlation coefficients from your sharp or casio calculator
Casio fx-83GTPlus calculator
Given the frequency table find the mean and standard deviation
| X | 1 | 2 | 3 | 4 |
| f | 5 | 7 | 6 | 2 |
(i) press Mode 2,1 you will see a table as below imput the data as shown .Make sure the frequency is on by pressing shift mode (set up) down curser 1.
(ii)To get the mean press AC
(iii)Then shift 1.(iv) then 4 (on 83ES use 5) then 2 for the mean = 2.25.
(v)Then shift 1.and 3 for the standard deviation = 0.94207.
| x | y | |
| 1 | 1 = | 5= |
| 2 | 2 = | 7= |
| 3 | 3 = | 6= |
| 4 | 4 = | 2= |
Data from a scatter Plot
| X Score (independent variable) | Y score(Dependent Variable ) |
| 5 | 20 |
| 8 | 18 |
| 6 | 22 |
| 7 | 28 |
| 10 | 27 |
| x | y | freq | |
| 1 | 5 = | 20= | |
| 2 | 8 = | 18= | |
| 3 | 6 = | 22 = | |
| 4 | 7 = | 28 = | |
| 5 | 10 = | 27 = |
(i) Press Mode 2 2 you will see a table as above imput the data as shown .
(ii) When all the data has been entered Press AC
(iii) Press shift 1 then press (5 (var) then press 3 (r= 0.4174 ) this will give the correlation coefficient
(iv)To get the information of the regression line press shift 1 then 5 then 1 (A)=16.19 this is the intercept of the regression line and the Y axis .Press shift 1,5 then 2 (B= 0.9459) for the slope of the regression line. The regression line is in the form y = 16.19+(0.9459)x {y = a + bx}
For Casio Fx-83ES
(iii) Press shift 1 then press (7 (reg)then press 3 (r= 0.4174 ) this will give the correlation coefficient (iv)To get the slope of the regression line press shift 1 then 7(reg) then 1 (A)=16.19 this is the intercept of the regression line and the Y axis .Press shift 1,7(reg) then 2 (B= 0.9459) for the slope of the regression line. The regression line is in the form y= A+bx
For the sharp 531 use the following metho
Sharp W531 Calculator and Statistics
The sharp w531 calculator can be used to find the mean and standard deviation as follows.
| X | 1 | 2 | 3 | 4 |
| f | 5 | 7 | 6 | 2 |
Method
(i) Press mode then pres 0 the screen reads STAT 0 (SD).
(ii) Input data as follows 1 (x,y) 5 Data (change) the screen reads DATA SET = 1 .
(iii)Then 2(x,y) 7 Data etc the screen will read DATA SET =2
When all the data has been entered the screen will show DATA SET = 4.
(iv)To find the mean press RCL 4 ( ) = 2.25
(v)To find the standard deviation press RCL 6 ( ) = 0.94207
To find the Correlation coefficient from a scatter plot using Sharp w 531 calculator.
| X Score (independent variable) | Y score(Dependent Variable ) |
| 5 | 20 |
| 8 | 18 |
| 6 | 22 |
| 7 | 28 |
| 10 | 27 |
Method :
(i)Press mode then press 1 SCREEN READS STAT 1 (LINE).
(ii)Input data as follows 5(x,y) 20 data screen reads data set = 1 . (as above)
(iii)Repeat for the rest of the data .after the last imput screen should read DATA SET = 5.
(iv)To find the correlation coefficient press RCL (DIVISION SYMBOL) =0.417
(v)To find the equation of the regression line (line of best fit)
(vi)To find the slope of the regression line pres RCL ) (RIGHT BRACKET ) = .946
(vii)To find where the regression line cuts the y axis pres RCL ( (LEFT BRACKET) = 16.189
(viii)Therefore the equation of the line of best fit is y = 16.189 + (0.946)x
The line of best fit is often written as y = a+bx
Project Maths Easter Revision Courses at Ballinteer Institute
Easter Revision Courses in Project maths (paper 2) will take place at Ballinteer Institute in Dundrum from 10th to 14th April. The course will be given by John Brennan and will include all the strand 1 and strand 2 topics. A full set of notes on all topics will be provided .Call Ballinteer Institute at 01-2960006 .
It has also come to our attention that maths grind schools have been set up by non teachers and others from the building industry claiming they are experts on Project maths .One of these tuition centres is passing off a well known Maths web sites notes as their own .
Students beware
Combinations no longer required for Ordinary Level Maths
In the new syllabus published in September 2011 combinations have been removed from the ordinary level syllabus .Bernouilli trials are still on.You cannot be asked the definitions of the differen types of data univariate etc . But you must be able to recognise them. Trig equations involving quadratics can be asked but you have to be guided through them.
Proofs of Junior cert Theorems cannot be asked !
Geometry and Project Maths (what not to study)
Many students and teachers are concerned about what geometry they must study for leaving cert Project Maths .
The following is a reply received from the SEC which clarifies the matter and should help teachers decide on what Geometry to cover.
The NCCA and the support service have received some enquiries on this matter. Accordingly, the NCCA has answered as follows on their website, and the support service have a link to the same text:
What synthetic geometry is required for Leaving Cert Maths candidates in 2012, 2013 and 2014 who opt for the alternative problem-solving question as provided for in Section 2.1 of the Leaving Cert Maths syllabus (page 22)?
For all candidates, whether opting for the synthetic geometry question based on section 2.1 (page 22) or the alternative question of a problem-solving nature, ‘knowledge of the geometrical results from the corresponding syllabus level at Junior Certificate is assumed’ – as stated in the introduction to Strand 2 on page 21 of the syllabus. For students sitting Leaving Certificate in 2012, 2013 and 2014, this refers to the geometry in the JC Maths syllabus they followed at junior cycle i.e. the revised syllabus which was introduced in 2000.
Knowledge from that syllabus at Junior Cert. together with the remainder of the Leaving Certificate Strand 2 (i.e. not including the new material of Section 2.1), can be expected to form the basis for contexts and problems associated with Strand 2 that may arise in Section B of the examination paper at Leaving Cert over the same period of years.
The SEC will ensure that the examinations conform to the above. It may be noted that there is no stated or implied commitment in the documentation to the location of this choice on the examination paper. However, it may safely be assumed that it will occur in Section A.
I trust that this clarifies the matter.
Kind regards,
SEC
What this means is that for Higher level Students the new geometry (Syllabus 2.1 Theorems,constructions,definitions)can only be examine in Question 6A and nowhere else on the paper .It is therefor possible to ignore all the new Geometry and just revise the Junior Cert Higher geometry. This will save a couple of weeks teaching geometry .It also means that questions on the centroid,orthocentre,cannot be asked except in Q6A Enlargements are not part of 2.1 therefore they must be covered.
For Ordinary level students just ignore the new geometry(Constructions,Definitions,knowledge of what the new theorems say) and practice Junior Cert Ordinary Geometry problems Note you cannot be asked to prove any theorems .
This is good news for all leaving cert students and teachers .
Making Project Maths Results look good !
Analysis of the Leaving cert higher results for the last 10 years show that the average mark (mean mark) is 67% with a standard deviation of 16% .The mean has not changed by more than 1% in all that time and the standard deviation has varied by less than 1% .
Analysis of the Leaving Cert H project maths for 2011 .
The average mark (mean mark) is 70.2% with a standard deviation of 12.87 .
Indicating that most people doing project maths did a lot better than those doing the regular exam .
Despite the fact that most students could not make head or tail of paper 1!
Interesting !
Project maths results credible ?
Extract from the SEC report on Project maths
LCH 2011 (project Maths) 90% get an honour (ABC) < 1% fail .
LCH2011 Higher maths regular paper 80% get (ABC) , > 3% fail
LCOrd 2011 (project maths) 76% get an honour (ABC) <7% fail
LCOrd (2011) regular paper 69% get (ABC) ,10% fail.
Marks awarded for project maths questions up to 50% higher than similiar questions on regular papers .
See the following example
Question 4a; Project Maths LC H 2011 for writing down the scale factor students were awarded 15 marks .
Leaving cert (Ordinary Level ) regular exam Q4c(i)2011 (yes 2011) for writing down the scale factor students were awarded 5marks. In leaving cert Ord 2005 and 2007 5 marks were awarded for writing down the scale factor.
Project maths students get 3 times as many marks as regular LC students for the same answer!
New Project maths Solution Books available Now !
Two new Solution Books for Ord and Higher maths available now.
Each Solution Book will contain
(i)Solutions of all SEC sample Papers 2010,2011 .
(ii)All NCCA Sample papers 2010,2011.
(iii) All actual exam papers 2010 (paper 2) 2011 (paper 1 and 2)
(iii)The “must know “files
(iv)The new syllabus and what is gone from the old syllabus)