For clarifications please ask. Email Jim Hogan ACC572 jimhogan2@icloud.com, Cellphone texts and calls 027 461 0702

Here is a quick

1. Do you have a data measuring and monitoring system that allows you select a student and see what NZC Level in mathematics they are predominantly operating within? Y/N

2. Do your current mathematics programmes for Y9/10 target NZC L4 and NZC L5 as the success criteria? Y/N

3. Have you checked out the Ministry information for the new NUMERACY and LITERACY requirements for NCEA? Y/N

4. Have you checked out the new NCEA Standards and Assessment Trial on the NZAMT website? Y/N

Session 4

Big Picture

My take on the

Do not state "Students need to learn how to sit assessments!". This is a ridiculous and unsubstantiated claim. Ask the students. It is about as ludicrous as having school examinations Mid Year and End of Year. Purpose? None. Stop doing it.

A Mathematics teacher needs to have a good degree with mathematics papers gained to at least Stage 1. A degree in mathematics and or statistics is ideal, being a passionate mathematics teacher, being interested and aware of the development and progression of key mathematical concepts, and understanding the learning process for 21C students. Not a lot really! Just kidding.... it is an huge expectation! Even after 25 years of teaching and another 20 years or so of advising I am still learning the best approaches to learning and the core connections in the subject. Noticed and outstanding to me is that passionate teachers generate student engagement and achievement. Like most human endeavour, the more you put into something the more you get out of it!

Success in Year 11 begins at Year 9 and 10. [Earlier actually but that is out of reach!]

Just what is important in each of the strands? No longer is their time to "cover" everything or every AO so some selection is necessary. What would you choose?

Find a buddy,choose a strand or logic or problem solving and list 9 to 12, or what ever you need,

Now write a sentence that describes the

Here is a document I wrote a while back where I tried to just that. Check what you wrote with mine. Be aware my list is not "THE ANSWER" just another version which could change if you asked me to do it again or I had a new set of students to teach.

Group Discussion

Discuss. Is there a concensus? Does there need to be? Will it vary with intake, teachers and region?

Year 11 success depends on these understandings and of course others. Year 11 success needs reading and writing ability. Year 11 success needs a bit of drive and a pathway. Year 11 students are much more mature and start to see need.

Focusing on the mathematics (and Statistics) however and remembering that when NCEA was introduced in 2002 the curriculum was "siloed" into standards. This approach isolated strands and separated them into topics about which

Thank goodness for that! I can now generate a geometrical context and ask measure, number and algebra questions. Yeehaa! But there are issues. Firstly...

Describe how you could connect Probability and Geometry. Be creative here.

OR

Describe how you can connect Measurement and Algebra.

OR

Describe a context which contains Number, Algebra, Measurement and Geometry.

Connecting the strands is good mathematics so as teachers we need reconsider our learning programmes and make sure this is built in. Hello Problem Solving.

One of the expectations when writing an assessment (NZAMT Writing Camps) was the context had to be "only in that strand or standard" and present "a problem" to be solved. This neatly eliminated a geometrical context which generates a number pattern and generalisations. BUT all that has been overturned now and looking at the NZAMT exemplar called "Whakaama" I see several problems to be solved, more scaffolding, different aspects all connected together as "an assessment."

I think we can still ask "a Problem" however, with out excessive scaffolding, and have a context that may well include several strands.

Go to the NZAMT website and find the Whakaama Assessment, do it or peruse the .ppt solution and make up your own mind about the effectiveness of the assessment and how you might grade a "solution".

This was a question that raised its ugly head when standards based assessment was introduced in the early 2000's.

Find a buddy and see if you can write a statement that describes or defines "What a problem is."

One of the critical aspects of "a problem" is that no help, indication, suggestion, direction as to the solution is given by the assessor (or teacher). The question can not suggest the pathway and neither can an over zealous teacher. The student must access their knowledge and skills, their reading and writing ability, their thinking ability and produce a solution for assessment. Simple replication of mastered skills is not solving problems. Reproducing from memory a well rehearsed and previously solved proof is not solving problems.

The current NZC, for all the Mathematics and Statistics AO's states " They will solve problems and model situations..." . Long may that remain. Not sure if any math teachers still remember the "prescriptive syllabus" full of skills and examples. A dreadful thing which prevented math development of almost every student for several generations. I suspect a lot of teachers ignored it as they should have done. The 1984 Burgundy Bible was a much more comprehensive statement and much more oriented to learning and teaching.

This is the current descriptor for the proposed Internal Math and Stat 1.2 standard.

https://ncea.education.govt.nz/mathematics-and-statistics/mathematics-and-statistics?view=learning

This is the descriptor for the new interpretation of Mathematics and Statistics. Remember, same NZC.

So keeping in mind all of this information and noticing it is now OK to ask "Problems" ....

Describe and try to form into a task a context from which assessment for 91945 could be made.

https://ncea.education.govt.nz/mathematics-and-statistics/mathematics-and-statistics?view=assessment

This link shows all 4 new standards and their descriptions.

I am trying to think of contexts which would be accessible to a Year 11 student, mathematics which would be up to NZC L6 and have solvable problems.

Horticulture, Agriculture, School Playgrounds, Cars, Pets, Decorating, Hobbies, Animal Care, Travel, Holidays, Friends, Grooming, Clothes, Cellphones, WWW, Weather, Road Safety, Sport, Recreation, Music.

Here are a few.

The Year 11 students I talk with and ask about interests seem very vague and uninformed. The teachers I talk with and ask about contexts struggle but do suggest more locally based contexts which do actually make sense to students. Here is one local contact in one school. I suspect this is going to become the norm for assessment of this standard.

The lunch area for the Year 11 students is currently a large piece of lawn with a few benches and a couple of BBQ tables. The Year 11 class wants to make it a nice area to enjoy and meet during break and lunchtimes.

Seeing this it seems to me that the internal standards lend themselves to overtime project work. There are three other examples https://ncea.education.govt.nz/mathematics-and-statistics/mathematics-and-statistics/1/2?view=activities here.Assessment Task

Come up with a plan to re-design the area.

Your plan will be scale drawn, have a theme, have a time line for development and include funding of material costs.

My view on an assessment grade is a broad overview of the intentions of the standard, I do not like check lists because they tend to be a list of a presumed solution by a teacher and not from the student. It is the thinking of the student that is to be assessed.

The big ideas in this standard are in Expanatory Note 1 and for Award of Merit are

The NZC Level 6 descriptor comes into play here as well. Teachers need to be aware and include learning around process and knowledge ideas.Use mathematical methods, applying relational thinking, to explore problems that relate to life in Aotearoa New Zealand or the Pacific region involves at least one of:

selecting and carrying out a logical sequence of mathematical steps

connecting different concepts and representations

forming and using a mathematical model.

Click on this image for an enlarged view.

Write an assessment statement or rubric that would help an assessor grade one of the examples or yoru own assessment example.

There are 4 standards, each worth 5 Credits, two internal and two external. https://ncea.education.govt.nz/mathematics-and-statistics/mathematics-and-statistics?view=assessment

91944 is about exploring statistical data and could involve simulation and probability. https://ncea.education.govt.nz/mathematics-and-statistics/mathematics-and-statistics/1/1?view=activities

Look at the example activities. It is pretty obvious this is going to be an overtime event, probably in a group. The usual comparative, relationship, simple time series, and probability are suggested mathematical contexts.

91945, see above.

91946 is a CAT or Common Assessment Task. It is about critical thinking in teh context of statistics.

91947 Demonstrate Mathematical Reasoning. The description clearly suggests what is required but again no exemplars are available yet. It is a paper based assessment.

Students need to be familiar with methods, i.e. procedures and reasoning related to the following:

Number & Algebra

manipulating and simplifying expressions

generalising properties of numbers and operations

inequations

quadratic and simple exponential equations

simultaneous linear equations with two unknowns

optimal solutions

relate graphs, tables, equations, and patterns

relate rate of change to the gradient of a graph

Geometry & Measurement

Pythagoras theorem and trigonometric ratios in right-angled triangles in 3D situations

properties of similar shapes

transformations: their key features (reflection, rotation, translation, and enlargement) and symmetry of patterns

angle properties of circles building on knowledge angle properties of polygons as well as intersecting and parallel lines.

I am pretty happy with the idea that the Award of NCEA L1 is not for everyone. I think all students who enter Year 11 at NZC L5 or above (See Session 1) do not need to be assessed and could use the year as a study year.

The students who are at NZC L4 will pass these standards and need to be interviewed as to pathways and need for assessment. A full load would be all four standards and that would be a comprehensive course.

The problems arise when there are NZC L2 and 3 students entering Year 11. This has always been the case and was teh reason for mathematics teachers developing "Waikato Maths" and "BOPMA Maths" in the Central North Region. Other Math Associations developed similar programmes.

Looking at these students they have taken 10 years to progress into the third level of the NZC in Mathematics. There are many reasons for this slow progression and schools will be aware of the reasons and will have tried their best. The Award of NCEA Level 1 is a perfect target for these reluctant and disadvantaged students. They will need all the mathematics and statistics they can learn and must gain Numeracy and Literacy. Each student will have a story and it should be the Dean and Teacher's priority to understand the situation for each student, and carefully and regularly monitor each.

They do not need to do all 4 standards. The two internals 91944 and 91947 would seem to be a minimum expectation. This course could be a year a project work and assessed likewise. It has to engaging and fun, have firm and fair guidance and be managed by a mathematician. These courses can be quite demanding and need the skills of a juggler. Teachers with strong empathy would be needed.

The best solution to this problem is not to have it all. Make sure your Year 9 and 10 courses progress all students to NZC L4 and above. I have never seen this success for any cohort in any school since 2002 when I started measuring.

This is a good question. There are now hubs, homerooms, classes, lecture halls and everything else as well. If a teacher can manage a large group of mixed ability students effectively then un-streamed may be feasible. A lot of progress can be made in 4 hours per week with a talented group and targeting Year 12 Algebra, Geometry and Statistics outcomes could well produce some exciting acceleration. Whatever schools and teachers decide please keep it all student centered. Whatever is decided it must be for the pathways and betterment of students. I value highly external competitions such as the Australian Mathematics Competition. My accelerate courses would be deeply focused on thinking and reasoning, being critical and literate. There are oodles of high level but appropriate mathematical resources on NZAMT, Brilliant, AMC, NZMATHS, (just to name a couple) and in existing text books already in departments.

Sounds a bit like the Star Trek "Where no man has gone before". As at June 2022 we do not know. Expect Year 12 and Year 13 to have 4xMaths and 4xStats standards at each level. Two internal and two external as in Year 11. The content will be the same as the existing standards but more connected. Not a lot will change. Students who enjoy mathematics will take the subject along with physics/chemistry if they are science/engineering oriented. Just make it fun and be a passionate teacher.