GloSS Data

Profiling: understanding the nature of the students' learning strengths and needs in detail.

GloSS is a NZ designed mathematics test to measure which strategies students use in mathematical operations (addition, subtraction, multiplication, proportion, ratios). A strategy is the mental process a students uses to resolve the problem given in the interview. The strategies a student uses then points to the stage level that student uses to calculate problems.

Thus teachers have a guide on where to go next when teaching mathematical strategies to students. It's not a perfect test as students with a lower grasp of language may struggle with their oral explanation on how they arrived at their answer. This could disadvantage the teacher who perhaps may unconsciously use a bit of intuition to judge the strategy the student used and whether it was correctly applied. That means small risks may exist with incorrectly attributing a student their stage in mathematical operations. It also disadvantage the student if the wrong stage gets applied.

Nevertheless, GloSS is a useful tool as it's a 'talking test' that steps away from the traditional 'do the test individually in silence' mode. It gives an insight to a students' thinking that more traditional testing methods fail to give. It challenges students to use language to articulate their thinking so others can understand - in itself a skill useful in the real world, both now and in the future.

A final point about GloSS is that it can disadvantage a lot of ESOL students (5/6 my target students) due to limited English spoken in the home because it's a language-based test and students may have clues how to solve a problem but are unable to explain it.

If we look at the Expectation for Number for The New Zealand Curriculum and the Mathematics Standards the target students should be working through Stage 7 Advanced Multiplicative / Early Proportional Part Whole.

Instead, a quick glance of the target students' GloSS test interview 2 as at 29/5/20 shows that all students have not reached the required standard and sit in the stage E5 to stage 6 range for addition/subtraction and multiplication/division. Poorer results are seen in the proportional/ratio where the students' score ranges from stage 2 to early stage 5. This is summarised in the table below. Work needs to be done in taking the target students to the expected stage 7 to develop advanced multiplicative and early proportional strategies as well as the advanced additive.

The poor results in proportions and ratios reflects inadequate mathematical language skills, and a lack of understanding of the mathematical concepts, especially for student D, an ESOL student who just arrived from the islands this year and is in his first year attending an English-speaking school.

	GloSS T2 2020
	addition/ subtraction.	multiplication /division	proportional /ratio
A	E6	E6	E5
B	6	E6	E5
C	E5	E5	4
D	6	E6	2
E	5*	E6	E5
F	6	E5	5

The Tasks: Addition and Subtraction

Task 12: Leanna counted 82 penguins on the beach. Later there were only 44. How many penguins had left the beach?

Task 9: Miriama scored 476 points on a video game. Deb scored 123 points on the same game. How many more points did Miriama score than Deb?

Task 6: I have 84 cards. I give 7 cards to my friend. How man cards to I have left?

The Analysis

Students B,D, E and F were able to answer Task 12.

E and F solved the task by rounding and compensation: 82-40=42, then 40-2=38.

B solved the task using the same strategy but her explanation is misleading, "took away 40 then there were 42 left, then added 2 which left me with 38." If we follow this line of calculation the answer is 44. In the real world her explanation would not be at all acceptable; for example, if chemicals were involved there would be serious consequences.
I am inclined to use my intuition that she probably meant to say 'subtract', rather than 'add'. I felt she knew how to solve the problem but her careless use of a mathematical word led to the error in her explanation. So I decided to give her the benefit of doubt and I did not penalise her. This shows the value of teaching students the importance of correct mathematical language use to explain their steps, so this should be part of any maths programme.

D who recently arrived in New Zealand used renaming strategy.

A managed to get as far as Task 9 and solved the problem using part-whole strategy.

C managed to solve Task 6 by using an early numeracy strategy of counting back, hence his stage E5.

*Although E was able to solve Task 12 he could not solve Task 9. He attempted to use his knowledge of place value and mentally added ones, tens and hundreds separately to get his unknown number, 123 + ___ = 276. His answer was 256. When asked how he got the answer he said he took 123 to get to 476 and it came out 256. Then I asked him to tell me what he meant. He said: 1+2, 2+5, 3+6 and that gives you 476. I asked if he was sure and he nodded instantly without thinking about what he had just said. I gave him some wait time to see if he would check his calculation mentally. The only value that has been added correctly is in the tens place, 2+5=7. Again, using my intuition about the student's response and reaction (or rather lack of) when he was given two opportunities to correct his logic and reasoning I scored him at stage E6 (due to a gap in his maths skills set) despite achieving Task 12. 

The Tasks: Multiplication and Division

Task 10: A pack of felt pens cost $8. How many packs of felt pens can you buy for $88?

Task 7: You have 30 balls to put into bags. Each bag can hold 5 balls. How many bags do you need?

The Analysis

Students A, B, D and E achieved Task 10.

Students B, D, and E used their multiplication facts to solve Task 10, (8x11=88 and 88/8=11) while A used a combination of multiplicative and additive strategies (8x10=80, 80+8=88).

C and F were not able to solve Task 10 but managed to complete Task 7. F used his fingers to ski count in 5s, while C explained that 5x30=6. I knew what he meant but did he realise what he said and did he also realise that his statement was not reasonable? Again as with Student B (addition/subtraction) and Student E (for multiplication/division), I used my teacher judgement to score him E5. He did use a multiplicative strategy but mixed up his product with the factor. Or alternatively he does not know nor understand the setting out of a multiplication equation. Like B and E, C needs practise in using appropriate mathematical language to explain his strategy. Although his answer was correct his explanation was not. 

As an assessor, I am after the correct answer and the strategy used. But I am also looking for correct language used. As teachers, we fail our students if we don't teach them to use mathematical language correctly. It it like teaching English to students and accepting their grammatical mistakes as being ok. It's not ok to accept inappropriate use of maths language.

The Tasks: Proportions and Ratios

Task 11: Which is more money: one-half of $20 or one-quarter of $40?

Task 8: The white piece is one-quarter of a strip. What fraction is the grey piece?

Task 5: These 15 players have to spread out evenly on the court. How many players should be in each third of the court?

The Analysis

F managed to get as far as as Task 11 by using unit fractions from subtraction facts.

A,B, and C completed Task 5. Students A used multiplication fact, E used division fact, and B used a lot of talking to help her solve the problem. Initially she said, "There is nothing because you can't evenly spread 15 people. 15 is not an even number so one has to stay out." As I was about the end the test, she continued talking and then realised how to solve the problem and, said, "If there were thirds then 5 people. I have 5 and 5 and 5." She used additive partitioning. 

Student C solved the problem by moving the images with his fingers and was not able to go further in the test.

Lack of understanding of the English language was a problem for D who was not able to complete any tasks. 

Given that GloSS focuses on language to show that learners understand how to solve maths problems, it's important that students can talk about maths concepts and tackle maths problems with appropriate language, knowledge and skill sets.

Where to Next

It's generally accepted that children working on a problem together in a group - and using appropriate language (example: what to say and how to say it), appropriate conversational structure (example: established rules on who can speak and when), with appropriate rules of politeness towards each other, tolerance for differing opinions, acceptance of differing abilities etc - get much more out of their learning than if they sit there working individually in a wholly teacher led mathematics activity. 

If a class lacks the necessary skills to experiment and succeed in student-led problem solving activities, it's the teacher's responsibility to give students the tools to effectively work together with appropriate mathematical language. This is not to say teacher-led  interactions with students is bad. After all, students cannot learn appropriate mathematical language without being taught. But it's equally true that student-student talk improves educational outcomes as well, and to be successful, students need to be taught structure: knowing what to say, when to say it, how to justify their strategy etc. This means first modelling exercises with students until they can use correct mathematical terminology to explain their approach. 

Secondly, the class needs to understand how to work together to reach conclusions in student-group-led problem activities. This process was enacted in a classroom that formed part of a study in a research paper titled, 'Teaching Students How to Use Maths Language to Solve Maths Problems', by Neil Mercer and Claire Sams in 2006.

In their research the targeted students showed that, "children with guidance and practice in how to use language for reasoning would enable them to use language more effectively as a tool for working on maths problems together."

Mercer and Sams points out "that improving the quality of children's use of language for reasoning together would improve their individual learning and understanding of mathematics." (p26,2006)

"More precisely, we have shown how the quality of dialogue between teachers and learners, and amongst learners, is of crucial importance if it is to have a significant influence on learning and educational attainment." (p26, 2006)

Mercer and Sams conclude "that the teacher is an important model and guide for pupils’ use of language for reasoning." (p26, 2006).

We do make a difference in the quality of our learner's education and we cannot underestimate our role in supporting them and helping them to improve their learning outcomes.

Basic Facts Data

Profiling: understanding the nature of the students' learning strengths and needs in detail.

Yesterday the students sat their Basics Facts test. This is a school-wide test carried out in Term 2, which assesses for accuracy. The students are given a total of 50 problems, 2 mins/column, a total of 4 mins.

The results are as follows: 

Target Students - Basic Facts 29/5/20
Student	addition	subtraction	multiplication	division	mixed
A	98%	94%	64%	30%	78%
B	94%	98%	62%	36%	90%
C	94%	88%	82%	50%	72%
D	100%	98%	84%	84%	92%
E	96%	94%	94%	84%	98%
F	100%	98%	74%	46%	92%

A quick look at the basic facts test shows that all students are solid on their addition and subtraction facts, except for student C who needs to work on his subtraction.  All students need to know their multiplication and division facts, while at least two need to work on their mixed facts.

A further analysis of their answers shows that I need to cover the concept and definition of zero in  multiplication  as three students (A, C and D) did not understand the purpose of zero - nothing - in multiplication. Student D consistently wrote his answer as 4 x 0 = 4, 5 x 0 = 5, 9 x 0 = 9, etc

Secondly, student D needs guidance in the concept of division and the division sign, as 7 of his divisions were treated as multiplication. Hence 3 / 3 = 9, 6 / 2 = 12, 8 / 2 = 16, etc.

Thirdly in another instance student C and E followed a pattern of operation rather than looking at the detail of the problem. They failed to observe that the operation had changed so they need to learn to notice, recognise and respond to the operation sign whether it is addition, subtraction, multiplication or division.

Fourthly, student C gets the right answer when dealing with zero in a singular list of subtraction basic facts and a second singular list of addition basic facts. But when the basic facts get mixed up with multiplication, division, subtraction and addition in the same list, he consistently gets the wrong answer in subtraction eg. 2 - 0 = 0. Addition was not a problem: when he adds 4 + 0, he gets the right answer.

Fifthly, students A, B, C, and F need to understand that division is repeated subtraction, division and  multiplication are the opposite of each other and that if they use their knowledge of multiplication facts they can easily solve division problems. A corollary of this could be the students don't know that subtraction is the opposite of addition and vice versa.

Numeral formation needs to improve for students B, E and in particular C who formed her digits poorly. It could be that they wrote hurriedly, or it could be that they need practices on how to write numbers. Regardless, it needs to be covered to reduce their error rate.

Lastly, while observing the students during their basic facts test, not one child checked or proof-read their work. In fact student C turned his test paper over, faced down after each test. While student A had given up during his division test and decided he didn't want to do anymore, hence his low score of 30%.

All the above issues need to be addressed and talked about with the students so they become aware of how they can improve on understanding their skills and techniques.

As a teacher of students who have learning needs I am not at all opposed to students knowing their basic facts. To me the issue of learning basic facts is less about what students should know, and more about how basic facts should be taught.

The traditionalist would argue techniques such as memorisation, rote learning, speed tests etc should be used because they have been proven by the test of time.  The modernist points to the importance of number strategies because it teaches students how to manipulate numbers rather than just memorise them.

Professor of Mathematics Education Jo Boeler, comes down firmly on the side of the modernist in her research, 'Fluency Without Fear: Research Evidence on the Best Ways to Learn Maths Facts'. She argues that "mathematics facts are important but the memorisation of maths facts through times table repetition, practice and time testing is unnecessary" and damages student's attitudes towards maths and their long-term understanding of it.

She argues that an adult who was taught their maths facts by traditionalists might say 7 x 8 = 54 when in fact it's 56. If they're unable to correct themselves, it's likely because they lack an understanding of how numbers fit together.

The student taught by a modernist may know that 7 x 7 = 49 and they have to add 7. Or they might know 7 x 10 = 70 and subtract two lots of 7 to arrive at 56. If the student makes an error, they can correct themselves using their knowledge of numbers rather than memorised facts.

The essence of the argument is that students learn their basic facts anyway without memorisation through the process of learning various mathematical strategies. Moreover, because learning number manipulation offers students a deeper understanding of how numbers fit together, it gives them a logical pathway towards higher level thinking.

However, on occasions we have to look inside ourselves because what works as a teaching tool for one student may not work so well for another. So it follows that memorisation and rote learning techniques for learning basic facts should not be completely abandoned. Instant recall of basic facts is a necessary skill to solve number problems especially in PAT tests where speed is required and where time is limited. Moreover as I have already mentioned in my earlier blog, basic facts is the core to the the various conceptual understanding and knowledge in mathematics (27 April) and so basic facts is a requirement.

Admittedly, as a teaching technique for learning basic facts, memorisation focuses primarily on two senses: the ear (as in chanting) and the eyes (as in flash cards and the like). It can be made more successful by adding in the kinesthetic sense (as in writing out the facts by hand in a frequent maths activity).

An even more successful approach uses all senses at once on a device. Susan Koscinski and David Gast claimed in their research, 'Computer Assisted Instruction With Constant Time Delay to Teach Multiplication Facts to Students With Learning Disabilities', that, "results indicate that the computer-assisted instructional program was effective in teaching multiplication facts to students", who have more difficulty in learning basic maths facts than "their other non-handicapped peers". Thus repetitive learning of basic facts has its place, and by extension, it can also benefit those of normal ability who gain more traction using memorisation and rote learning techniques as well.

Hence, one of the teaching tools I will be using to help my learners to increase their basic facts knowledge and their speed of recall will be the use of online interactive programmes.

Target Students Chosen

I started the year with an idea who my target students were going to be. Then Covid-19 came along and threw that idea out the window. I found myself time constrained and not being able to wait any longer for my actual target students to begin attending school, so instead I selected target students based on who turned up at school today during our Lockdown Alert level 2. These are year 7 students and all of them have maths learning needs - some considerably more than others.

Today I carried out GloSS testing and Basic Facts on these students. The results will be analysed over the weekend.

Collecting Data and Evidence

Begin to collect evidence and data and come to the next session ready to share your preliminary findings about the nature and extent of the student challenge i.e. using your baseline students data and evidence.

On Tuesday 23 March the government announced that the Education sector would be going into Alert 3 Lockdown. At the time I had planned to do GloSS, Basic Facts testing as well as conduct a survey, all to be completed by the end of Week 8 of Term 1. This did not happen.

The PAT testing was completed well before the Lockdown and I am still waiting for the results to be imported from NZCER marking to our SMS.

Therefore, I have at this moment no evidence nor data to share.

I tried to conduct a survey during a Hangout Meet this week but only one child turned up and then he quickly left. At another meet there were only 2 students. Moreover, I am unable to reach half of the students who have no access to a device during the Lockdown.

I have decided that it is not a feasible task to undertake and I hope to complete the survey when all the students return to school, as well as testing them.

Tools, Measures and Approaches

Describe the tools/measures/approaches you plan to use to get a more detailed and accurate profile of students’ learning in relation to that challenge. Justify why you chose these approaches and tools.

To get a more detailed and accurate profile of the students' learning I need to think about the different assessment tools available to me and the methods I need to use to acquire information about student learning. These methods include both formative and summative.

Available summative assessment tools at my school include:

• PAT maths
• GloSS
• Basic Facts
• pre and post assessment

PAT, GloSS and Basic Facts are school -side test that are conducted twice yearly at our school and has been part of the summative school assessment for a very long time.

PAT Mathematics "helps teachers determine their students' levels of achievement in the knowledge, skills and understanding of mathematics in the New Zealand curriculum. It is directly alined with the New Zealand Curriculum and targets the big ideas students need to understand in order to make progress." (Source: NZCER PAT Mathematics)

While GloSS, "provides a series of questions to identify the strategy stage a student is operating at on each of the three startegy domains of the Number Framework." (Source: NZmaths Assessment tools)

Lastly, basic facts is a necessary test to carry out. If we look at the basic facts concept map, we see that basic facts is the core to the various conceptual understanding and knowledge in mathematics.

(Source: Assessment Resource Banks)

Pre and post test: I like doing pre-test because I can find out how much knowledge the students have before the start of their maths topic learning while post-test has a dual purpose. For the student, it is to see if they have increased their knowledge and understanding of their learning and for me, to see fi my teaching approaches and programme are appropriate and challenging.

As for the formative assessments they include:

• survey
• observation
• feedback
• conferencing
• workbook
• OTJ

Its' important to know how students feel about maths and a simple survey of their thoughts and attitude can reveal a lot about the issues and problems students face with maths.

As teachers we regularly observe and evaluate our students in many different settings. We look at behaviours and actions, and we listen to the conversations that take place in and out of the classroom. When we are in the classroom our eyes are constantly roving making sure every one is learning and on task and everything is fine.

I like using feedback because it helps students to focus on a particular knowledge,, skill or strategy that needs to improve and corrected.

I also like conferencing because it give me time-out with each student. It allows me to get to know the learner, understand the finer details of the learner's knowledge and skills and to cater to the learner's needs.

Going through a learner's workbook is also important as it allows me to see where the missteps are in a learner's strategy, method or calculation and to pinpoint learning areas that need to be worked on.

Lastly, bu combining the aforementioned summative and formative assessments, I can more accurately make an OTJ about my learners during report writing time.

Focus for the Manaiakalani Collaborative Inquiry

Task: Collaborate with your school’s leadership team and colleagues to identify areas where your inquiry will make a powerful contribution to wider school and cluster goals.

During a discussion with the leadership team we decided that due to the poor outcome of our students' achievement in Maths, my inquiry should focus on the year 5-8 senior team where the results showed a gap in the students' learning and hopefully my teaching as inquiry method will make a difference to our students' learning.

This focus aligns with Manaiakalani's Collaborative Inquiry number 6, 'lift the achievement in maths for all students years 1-13'.

My team and I want to find out what caused the gap in our data at the end of 2019.

There will be a lot of issues I will look into such as our school structure, school resources and equipment, teacher understanding of content and curriculum, the existence of a differentiated teaching programme in our school, professional training, delivery of the full maths curriculum, engagement by students and teachers, teacher reflection and evaluation of appropriate teaching practice, student voice and so forth.

Once we have decided what factors contributed to our poor student academic outcomes, we need to put in place an intervention plan that resolves these issues.

For an investigation to be successful I need the support of the teachers. I put this idea forward to our colleagues in the staff meeting and they were happy to support me in this Inquiry.

An Inquiry Stocktake

Use the ‘inquiry stocktake’ doc to reflect on and write about what you aim to learn about inquiry this year.

Identifying valued learning outcomes (VLOs) to focus on:
My aim here is to learn about, with other colleagues in the Manaiakalani community, what the best learning outcomes for our students at Ruapotaka would be. I'd like to hear their viewpoints, ideas and feelings about how they identify their outcomes and why they have chosen a particular outcome.
Profiling students’ learning in those VLOs:
Here I want to know who our target students are and to track both their progress and achievement over time.
Generating hypotheses (especially teaching):
I have my own thoughts what the hypotheses might be and I would like to know if similar hypotheses have been generated and how successful were they in their conclusion.
Testing hypotheses (investigating school senior team teaching):
This is an area I am looking forward to and I hope that sharing and talking to my colleagues both within my school as well as my colleagues within the Manaiakalani community will help me understand what is going on with our students at Ruapotaka.
Using research literature and other sources to identify more effective approaches:
Data is easily accessible and offers guidelines towards our students academic achievement. My biggest concern is gaining access to readings especially those from the University (which is not so easily accessible unless I am a student) to gain a better understanding of the issues going on with our students at Ruapotaka.
Implementing new approaches:
We currently have staff who have not had Professional Development (example: maths PLD) and we need to create a consistent teaching approach that involves a variety of methods, programmes that are challenging and targeted, regular data analysis and to take a hard look at ourselves as teachers and professionals.
Monitoring (and tweaking) new approaches:
Through this inquiry I want to know if my hunch that student achievement improves when consistent teaching approaches get used across the school (such as differentiated teaching approaches, talk moves, regular monitoring of students, regular self-reflection, analysing data for where to next) have merit.
Evaluate shifts in own teaching: Using data, my colleagues teaching techniques, self-reflection, children's feedback etc.
I hope that the approaches I take benefit the students. I feel if I follow the inquiry model, do my readings, talk and share with my colleagues, hopefully I will have made a difference to our students.
Evaluate shifts in student learning:
This is the part I normally feel anxious. Have I done my job well? Did the students make a shift? How much impact did we make? Will the students new learnings stick?
Keep a clear and detailed record of all stages of inquiry:
Like any scientific research that involves a hypothesis, a detailed journal account of the stages, procedures and process that I have taken is recorded with accuracy and with evidence so that others can learn from my inquiry.