Do We Have Standardised (Average) Children?

 As a teacher from 1965 and then a Maths Adviser from the 80's, finishing up as a Private Maths Education Consultant, we were encouraged and expected to teach on the basis that New Zealand had a Child Centred Education System!

THE 'NOW' POSITION 

In the 70's while teaching at Intermediate Schools in Auckland we often called on the Mathematics Advisers to demonstrate in our classrooms or work with them at In-Service Courses. (Jock Day in Auckland, Joan Paske in Wellington etc) In their work they encouraged us to find the "NOW" position of the children and then prepare programmes to build on what they knew.  This often involved some sort of grouping both streamed and cooperative.

RICH MATHEMATICAL ACTIVITIES  Lead to Differentiated Teaching and Learning

In the 80's led by Murray Britt, lecturer at Auckland College of Education (also writer of the 1990 Maths Curriculum) encouraged us all to have our students involved with Problem Solving and Investigations.  Many of these activities were what were called "Rich Mathematical Activities".  An activity that most(all) students could start but were "open" so that more able students could explore further.

At and Auckland Full Primary School (about 2012) they instituted a two year Professional Development Programme focussing on Problem Solving and Investigations, and meeting individual students needs. The visiting Maths Consultant visited fortnightly demonstrating in classrooms and giving feedback and advice for teachers, as well as whole group Inservice. This programme ran for just over 2 years.  Towards the end of the 2 years a call from the local Secondary school to the Principal ask "what are you doing differently in maths as your students are head and shoulders above students from other Contributing Schools.

DO YOU WISH TO BE COMPARED TO A 35 YEAR OLD RUNNER?

In my capacity as an Adviser/Consultant I was often asked to speak with the Parents of schools "about Maths" A very common question/comment was "why do you have students working at different levels, rather than like when I was at school?"

My response often included an Analogy similar to this?  

        "Peter Snell is a 37 year old athlete running the 800 metres"

        "Please stand up if you are Between 35 and 39"

        "If you were in a race with Peter Snell, as we are all "equal" I expect you to be close to Peter at the Finish Line!"

        Is that a fair race?   Why then do we expect 30 children in a class to be at the same level of Maths when they have had different pathways to Standard 5-Year 5?

IS THIS FAIR?

 

Why do I read that the Education System is now instituting the same maths for all students of an Age Group, regardless of the different pathways they have travelled to get there? 

I have been watching in dismay at what has been happening in Mathematics Education, over the past years. Achievement levels have been falling regularly, so each Govt will try and put their answers to the problem into place.  

Where has been the outcry for what is happening at the moment?

Children are NOT Standardised, Average, or at the same level, so dont teach them as if they are!!

CHECK OUT THE NEXT BLOG ABOUT STUDENTS BEING AVERAGE! 

Which Trees and Plants?

 A simple survey leading to a presentation for the school or parents etc.

Spiralling Under Control

 This is card #4 in the series, more to come in the next few days.

I would appreciate any feedback about how useful the cards/activities are 

 

 

 

 

 

 

 

Catlin's Special Plants

* This activity could be an introduction to algebraic rules. 

* When I was at school Algebra was a topic on its own, often not related to anything real or "concrete".  To me, Algebra is about generalisations of patterns and numbers around us.  

* "Rules" we may have learnt about numbers are the beginning of Algebra.  e.g. When we muliply a number by 10 we shift the numbers one place to the left and put a '0' in the 'ones' place, NOT 'Add a Zero' as adding zero doesn't change the number!!!!

* We want and need to students who understand and can apply those understandings to other situations. This means not just teaching rules nand short cuts but using investigations and thinking to develop understanding.

 

 

 

Can You Measure The Height of a Tall Tree?

The Second card in a series of practical maths explorations.  They are designed to be printed on card and students-groups or individually- explore and explain their investigations.

 

Bet you cant organise this garden

 The idea for science/maths cards arose about 2009, when a Homeschooling Parent and Science Teacher, who was going to Publish them, asked Helen Walters and I to create "stand Alone" Maths/Science Cards.  Many cards were created but too my knowledge were never published.  So I have tweaked and will now publish via the Blog many of these cards.

All cards are of an Investigative Nature and can be completed individually or cooperatively.  We would encourage a cooperative approach as this gets the students discussing ideas in maths and science.

Feel free to print off but please acknoeldge where they are from. 

Reading and Maths

 An interesting comment by Charlotte Wilkinson, "The Wilkie Way" why we need to see reading as part of mathematics learning.

I would also like to suggest that we help students learn "How to read Maths and Science Material" as it is different and requires different comprehension to the usal prose we use for teaching reading

www.wilkieway.co.nz
Maths and Reading

How many times have I heard teachers saying “we are assessing maths not reading”. The teaching profession has failed to recognise that reading is an essential part of using mathematics in our everyday lives. Principals are now alarmed by the low pass rate in exam trials with year 10 students. They acknowledge the mathematics is at about the right level but the students are unable to access the maths because it is “buried” in words.
This is nothing new and researchers around the world have been saying this for years. For this newsletter I am referencing an article from the Journal of Mathematics Education June 2011 Vol 4 No 1 titled;
Maths Literacy: Are we able to put the mathematics we learn into everyday use?
(Bobby Ojose University of Redlands USA)
Maths literacy is the knowledge to know and apply basic mathematics in our everyday living. An important part of maths literacy is using, doing, and recognizing mathematics in a variety of situations. In dealing with issues that lend themselves to a mathematical treatment, the choice of mathematical methods and representations often depends on the situations in which the problems are presented.
To effectively transfer their knowledge from one area of application to another, students need experience solving problems in many different situations and contexts.
The OECD publication, Measuring Students Knowledge and Skills (OECD 1999) lists the types of texts as part of reading literacy, which in part determines what constitutes mathematics literacy.The publication mentions as examples texts in various formats:

Forms: tax forms, immigrations forms visa forms, application forms, questionnaires;

Information sheets: timetables, pricelists, catalogues, programs

Vouchers: tickets

Certificates: diplomas, contracts etc

Advertisements

Charts and graphs, iconic representations of data

Diagrams

Tables and matrices
Inorder to comprehend most of these types of text you need to bring knowledge of mathematical skills.
Here is a list (Not exhaustive as knowledge is dynamic and technological advancement is forever changing)
Everyone should:

be able to perform the basic operations of addition, subtraction, multiplication and division with whole numbers, fractions and decimals.

know concepts such as ratios, percentages, roots, square roots, absolute values, reciprocals and exponents.

should know the metric measures of length, area, volume, mass, time and temperature and how to convert between the measures,

understand simple linear equations, plotting graphs of linear equation, slopes,

know operations with positive and negative integers

know the concept of proportional reasoning.

should know the various area and circumference formulae for circles, squares, rectangles and
triangles.
• be familiar with cartesian co-ordinate system in two and three dimensions,
• be able to convert size on a scale model or map to actual dimensional size.
• be able to do basic construction using a compass and straight edge.
• should be familiar with three dimensional shapes in terms of finding volumes and surface areas of
shapes like cone, pyramid, prism, cylinder and sphere
• be able to find the measure of central tendancies when given a set of values
• be able to graph and interpret data as a histogram, pie chart, bar graph and line graph
• know probabilities based on theory and probabilities based on experiment
• compare risk factors in different situations
All of this list falls within levels 1 - 4 of the New Zealand curriculum and many of our students have the
mathematical knowledge so why are they still mathematically illiterate?
This will come down to pedagogical practice and a focus on the competencies required for mathematical Literacy:

Right from year 0 we need to be considering:
Mathematical communication: expressing oneself in a variety of ways - oral, written, pictures, diagrams; understanding someone else’s work.
Representations: Decoding, encoding, translating, distinguishing between, and interpreting different
forms of representations of mathematical objects and situations as well as understanding the relationship
among different representations. (Materials are not because young students are kinesthetic learners)
Symbols: Building an understanding of using symbolic, formal, and technical language and operations
Problem posing and solving: Posing, formulating, defining and solving problems in a variety of ways
Thinking and reasoning: Posing questions characteristic of mathematics, knowing the kind of answers
that mathematics offers, distinguishing among different kinds of statements; understanding and handling
the extent and limits of mathematical concepts.
Mathematical Argumentation: Knowing what proofs are; knowing how proofs differ from other forms of mathematical reasoning, creating and expressing mathematical arguments
Tools and technology: Using aids and tools, including technology when appropriate.
Unless we get back to actually teaching mathematics and not relying on computer programmes or apps for students to teach themselves, we will not solve the problem of mathematical illiteracy.
I sincerely hope the common practice model that will underpin our new curriculum “refresh” will place an emphasis on these competencies as well as a sequence for developing the knowledge and skills.
A sequence for knowledge and skills across the curriculum is relatively easy for mathematics as it is a
fairly hierarchical subject. It is important to make connections between topic areas as seldom does a
mathematical topic exist in isolation in the real world. Any sequence of work must provide the opportunity for explicit teaching, practice, application, discovery, and transfer.
No one resource will provide everything that should be included in your mathematics programme but
having a clear sequence will ensure continuity and progression.
A good resource provides opportunities for explicit teaching, practice, application, discovery and transfer built into the design. Along with a focus on appropriate reading levels to develop reading comprehension including the building of mathematical specific vocabulary.
The Figure it Out series is a greatly under used resource (because it is not user friendly) that will really
focus teachers and students on the need to develop mathematical literacy.
Maths Aotearoa + Wilkie Way + Figure it Out + NZMaths = A great maths curriculum to support the
teaching and learning of mathematics in New Zealand schools.