2023 - SESSION 1 Measuring and Monitoring Junior Students
The information on this page is my interpretation of what I notice and reason. It is designed to be of use to teachers to help them ponder, reflect and redesign learning programmes as required. Use accordingly.
For clarifications please ask. Email Jim Hogan ACC572 jimhogan2@icloud.com, Cellphone texts and calls 027 461 0702

Here is a quick SELF CHECK for your Math Department or the one you work within.
    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 1

The time for this session will be variable and depend on how well a Department has developed a robust measuring and monitoring system that is used and appreciated by teachers. Key to this system is a collective will the Year 9 teachers to get a good estimate of each student's numeracy ability or preferred or observed NZC level which a student operates at usually. There is a lot of dialogue that has to happen to ensure the Counting, Adding, Multiplying, Proportional and Critical Thinking Stages are appreciated and recognised by every teacher. Here is a link explaining the thinking. The NZ Numeracy Report 2004 has a summary of the thinking in Appendix D There was huge amount of time and effort and money spent during that project and it is a wealth of information in these reports.

Lets GO!
1. Measuring and Monitoring
Getting students into NZCL4 or "being multiplicative" has been a mantra of mine for 20 years. A student must progress through NZC L4 to access NZC L5 and NZC L6.

This means teachers must have a good understanding and being able to recognise thinking at each level to make an informed OTJ. Otherwise you have to rely on standardised assessment like e-AssTTLe, PAT or my favorite LOMAS. A good source of questions at specified NZC Levels is on the nzmaths.co.nz website and in the Learning Progression Framework. Remember it is not the question that determines the thinking a student uses, it is the answer the student presents. An hour or so should be all that is required for a teacher to be able to explain to another teacher the NZC Level any student response suggests. I once said "If a solution smells of addition it is probably NZC Level 3". Level 5 thinking is operating using fractions and decimals. Level 4 can involve simple fractions operating on whole numbers.

Briefly, one numeracy measure in each term that indicates the preferred thinking level a student demonstrates in solving number problems is all that is needed. This allows cohort, class and individual profiles to be created and predictions to be made. The optimum time to make a judgement on this ability is in the middle of the term, in the middle of a week and in the AM. Hence, Week 4,5 or 6 on a Tue, Wed or Thurs morning. An OTJ, by an informed teacher who notices what students do is an OK replacement for the judgement. Do not overlook the Year 8 information on Numeracy which is passed to the secondary school upon enrollment. The Year 9 Dean is the contact TIC here. Transfer the judgement the Intermediate contributing school has given the student (Stage 7 = NZC L4) and use this as a data point in the Year 9 overtime spreadsheet. There is usually good agreement with the new judgements in Year 9.

The colour bars progress from left to right Term 1 to Term 4. One measure per term.
The cohort picture shows clearly about 35 L2 and L3 students at the end of Year 10 who will struggle in NCEA L1.
These students need special attention to help them gain numeracy and for them NCEA L1 is a viable qualification.
The NZC L4,5 and 6 students will pass the on-Line Numeracy Assessment and can use Year 11 as a learning year. with no other assessment. 

This class shows the progression in learning as the year happens. EA1 and LT 1 were e-Assttle and Lomas results from Term 1. The Term 4 assessment was not completed.
The patterns become obvious over time. Term 4 could have been an OTJ.

In a different project school the MULT% or percentage of students at NZC 4 or above increases as the year progresses.
The mean NZC Level is a construct that serves to show how learning is progressing. A positive slope is necessary!


The school and student identifiers have been cropped from the last image which shows individual student performance. "Stepping up" is good. Flat top is not good but could indicate progression within a level.
Learning is messy and this "skyscraper" graph often shows students popping up and down as the year happens. Is there a reason or explanation?

A robust measuring and monitoring system must be established and nurtured. Teacher need to know how to make reliable OTJ estimates. A relentless focus on being multiplicative must be the junior year goal for all.
I would measure a math department's success by the multiplicative level of the cohort. Anything over 80% is very good and would build a strongly academic senior school.
One session of a project would be around building the measuring and monitoring capability including NZC progressions, teacher OTJ estimates, and recognising multiplicative thinking.

To Do
1. Develop and ensure all know, understand and use a robust measuring and monitoring system in your situation
2. Select some problems on LPF and give to students. From their answers decide what level of thinking is present and explain this to another teacher. Discuss of course.
3. What can you display in your classroom to help remind and focus students on being MULTIPLICATIVE?
4. What measure can your department as a target for students, class and cohorts?

Microsoft Word - Document5