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## Comp08.pdf

Te Poutama Tau Student Performance in asTTle
This study examines whether students participating in Te Poutama Tau transfer their knowledge to solving problems that differ in form and context. Additionally, it examines how these students perform in traditional written-type tests, in particular the asTTle test1, against the national norms for Màori-medium schools. An asTTle test was given to one cohort of year 4 and one of year 7 students who had participated in Te Poutama Tau, and the results were compared with those of a previous study2. In this test, both cohorts of students performed above the national norm for Màori-medium schools on number knowledge items. However, across all test items, both the 2007 and 2008 year 4 cohort performed below the national norms for Màori-medium schools. On the other hand, both the 2007 and 2008 year 7 cohorts performed above or close to the national norms for Màori-medium schools, although not noticeably so in algebra.
Initiated as a pilot in 2002, Te Poutama Tau is the Màori-medium component of a key government initiative aimed at raising student achievement by building teacher capability in teaching and learning numeracy in schools (Christensen, 2003). Te Poutama Tau acknowledges professional development as a key to integrating theory and practice for quality outcomes in Màori-medium mathematics (pàngarau) education (Trinick & Stevenson, 2006, 2007). By improving the professional capability of teachers, students’ performance in numeracy is also improved (Christensen, 2003). The Number Framework (Te Mahere Tau) is central to Te Poutama Tau. It outlines for teachers the stages of number knowledge and the operational strategies through which students progress in their learning of number (Ministry of Education, 2007a). Students are assessed against the stages of Te Mahere Tau using a diagnostic interview (Te Uiui Aromatawai, Ministry of Education, 2007b), which stresses conceptual understanding and students’ internal construction of mathematical meanings (Trinick & Keegan, 2008).
Research to date based on the data from diagnostic interviews indicates that Te Poutama Tau has improved outcomes for students (Trinick & Stevenson, 2005, 2006, 2007, 2008). This study examines whether Te Poutama Tau students transfer their knowledge to solving problems that differ in form and context. Additionally, it examines how these students perform in traditional written-type tests, in particular the asTTle (Assessment Tools for Teaching and Learning [He Pùnaha Aromatawai mò te Whakaako me te Ako]) test, against the national norms for Màori-medium schools. As a result of an earlier Te Poutama Tau/asTTle study, questions arose as to the validity of the asTTle norms for Màori-medium schools and whether the students’ results in that study would be consistent with those in future studies (Trinick & Keegan, 2008).
AsTTle is an educational resource for assessing literacy and numeracy (in both English and Màori). It provides teachers, students, and parents with information about a student’s level of achievement, relative to curriculum achievement outcomes3, for levels 2–6 and national norms of performance for
1 asTTle: Assessment Tools for Teaching and Learning (He Pùnaha Aromatawai mò te Whakaako me te Ako)2 Trinick & Keegan, 20083 The asTTle tests used in this study were based on the 1992

*Mathematics in the New Zealand Curriculum *(Ministry of
Education, 1992). All references in this paper to the curriculum or to curriculum strands are to this 1992 curriculum document.

Findings from the New Zealand Numeracy Development Projects 2008
students in years 4–12. Teachers can use asTTle to create “paper-and-pencil” tests of 40- to 50-minute duration, which means that students must be able to read and write. After the tests are scored, the asTTle tool generates interactive graphic reports that allow teachers to analyse their students’ achievement against curriculum levels, curriculum objectives, and population norms (for example, see ﬁ gures 1 and 2 in this paper).

What aspects of the asTTle test did Te Poutama Tau students perform well in and what were the gaps and areas of weakness?
How do Te Poutama Tau students’ asTTle data compare with the asTTle national norms for Màori-medium schools?
How do these results compare with the students’ performance in the 2007 study?
Two schools agreed to participate in the 2008 study; one was from a large city and the other was from a small rural town. Both schools had recently participated in Te Poutama Tau. The aim was to replicate the 2007 study as closely as possible, so it was decided to continue focusing on year 4 and year 7 students.
In the 2007 study, year 4 students had been selected because this is the youngest cohort that can be reliably tested using asTTle. Additionally, earlier Te Poutama Tau studies showed a considerable dip in student progress that began in year 3 (Trinick & Stevenson, 2006, 2007). Why this was so is not entirely clear. A number of reasons were considered, including the fact that this is the age group where students are possibly moving towards part–whole thinking. It is also the age group where students may be exposed to a change in teaching pedagogy as they move from years 1–2 to years 3–4 (Trinick & Stevenson, 2007).
The 2007 year 7 cohort had been chosen to provide a comparison with year 4 for showing differences and similarities. Also, schools could use the data when the students were in year 8 to focus on gaps and areas of weakness before the students went on to wharekura (Màori-medium secondary schools) or to English-medium secondary schools.

An asTTle test focusing on number was generated for each year group in the study, and test scripts were sent out to schools for trialling. The two tests consisted of 32 test items, which were selected to cover number items from the Number and Algebra strands. The aim of the testing was to gain maximum information on students’ performance on number and other items relevant to Te Poutama Tau. The nature of asTTle is such that individual test items cannot be selected without losing the capability of the asTTle tool to generate national norms (because norms are not available for individual test items) and associated data. The items in the 2008 test were not identical to those in the 2007 test, but both tests included test items that linked to the same Number and Algebra achievement outcomes in the curriculum. Measurement items were not included in the 2008 test; these were replaced by extra Number and Algebra test items because Te Poutama Tau has tended to focus on these two strands of the curriculum.

Te Poutama Tau Student Performance in asTTle
The test scripts returned by each participating school were marked, and then a report was compiled for each school. This report included four major reports for teachers, each of which provided different analyses of each year group. These analyses included:
comparing student performance against a nationally representative Màori-medium sample;
comparing student performance in relation to curriculum levels and difﬁ culty;
identifying curriculum outcomes that students had or had not achieved and which of these the students showed strengths in or revealed gaps or areas of weakness;
allocating each student in a particular curriculum level as being either at the beginning, proﬁ cient, or advanced stages.
This report was ideal for assisting teachers to group their students.

All results reported in this section are based on the aggregated results of the 2008 year 4 and year 7 students and are displayed using three types of reports. The results are compared with those from 2007 to identify patterns in achievement.

The asTTle reports are primarily aimed at answering the feedback question “How are Te Poutama Tau students doing in comparison with similar students in Màori-medium settings nationally?” AsTTle answers this question by providing comparative or normative information for the group of students in this sample.

Student achievement by year is shown in box-and-whisker plots that display both the national Màori-medium norms and the distribution of the student scores. The reports show the average of the year group and the range of achievement of that group. The box-and-whisker plots are based on ﬁ ve score points (top score, upper quartile, median, lower quartile, and bottom scores) attained by students participating in the test. The white box plot represents the performance of the 2008 Te Poutama Tau students, and the shaded plot represents the performance of the year 4 and year 7 national Màori-medium reference population. Groups that have short ranges within the box and/or the whiskers are more similar in their performance than those with wide ranges. Groups whose median scores are at the top or bottom of the reference group box (the student cohort in this study) probably differ from the national Màori-medium norm by more than chance.

This report shows the aggregated results for each strand of the curriculum that was selected for these particular tests. In the tests generated for this 2008 study, only test items from the Number and Algebra strands were included (as noted earlier).

These reports were identiﬁ ed by generating learning pathway reports to answer the question “What are the strengths and weaknesses of student performance in regard to the curriculum outcomes?” A percentage is given of the student cohorts that were identiﬁ ed as having achieved/not achieved

Findings from the New Zealand Numeracy Development Projects 2008
or as having strengths/gaps in regards to the curriculum outcomes. For this report, “achieved” and “strengths” have been aggregated and are reported under performance highlights. This is where more than 60% of the cohort was identiﬁ ed as having achieved and showed strengths in this outcome. “Not achieved” and “gaps” are aggregated as performance concerns. This is where more than 60% of the cohort was identiﬁ ed as having not achieved and as having gaps in their knowledge.

Comparison of the 2007 and the 2008 Year 4 Students

**Group performance**
The aggregated data of all the 32 test items shows the average of the year group and the range of achievement of the group. Figure 1 shows that the 2008 year 4 Te Poutama Tau students’ median in this study was slightly below the norm for students in Màori-medium schools. However, this is an improvement on the 2007 results, which were approximately 200 points below the national Màori-medium norm (Trinick & Keegan, 2008). The results for both these cohorts were not expected. The national Màori-medium norms were established before the implementation of Te Poutama Tau, so it was assumed that, because Te Poutama Tau predominately focuses on Number and, to a lesser degree, Algebra, these Te Poutama Tau students would generally perform better than the national Màori-medium norms in these two strands of the curriculum.

**20074 2008**
**Pàngarau Scale**
**Pàngarau Scale**
*Figure 1. * Group performance of year 4 students in 2007 and 2008

**Curriculum functions report**
Figure 2 shows that the 2008 year 4 students were slightly above the national Màori-medium norm in Number and below for Algebra. Again, this is an improvement on the 2007 results, where students were close to the national Màori-medium norm in Number but were substantially below the national Màori-medium norm in Algebra.
4 See the explanation on page 41 of the shadings of the box plots.

Te Poutama Tau Student Performance in asTTle

**2007 2008**
*Figure 2. *Year 4 student performance in the strands of the curriculum

*Learning Pathways Report for Year 4*
**Performance highlights**
**Number**
The year 4 students in the 2008 study performed positively in the questions that involved ordering whole numbers and decimals. Similarly, student results were positive in questions that required recalling basic facts for addition and subtraction. Number word sequencing and basic facts are both key components of the knowledge domain of Te Mahere Tau in Te Poutama Tau.

**Performance concerns**
**Number**
The 2008 year 4 students performed poorly in the questions that involved writing and solving whole- and decimal-number word-story problems with combinations of +, –, x, and ÷. This gap in achievement is consistent with the 2007 results.

**Algebra**
Both the 2007 and 2008 cohorts of year 4 and year 7 students performed poorly in most of the Algebra questions, including using the mathematical symbols =, <, and >. These also included questions that required entering either the correct symbol or quantity to show a relationship. For example, students were required to enter either <, >, or = in the box to show the appropriate relationship between 80 and 90 (80 90) and the relationship between the multiplication pairs 9 x 2 and 6 x 3 (9 x
They also needed to enter the quantity missing in the box in + 8 < 10.
Making, describing, and using rules for number and spatial patterns is also an area where a substantial number of 2008 students were below the national Màori-medium norm.

**Group performance**
Both the 2007 and 2008 year 7 Te Poutama Tau students performed noticeably better than the national Màori-medium norm (Figure 3). The range of performance is much narrower in 2008, suggesting

Findings from the New Zealand Numeracy Development Projects 2008
that most of the Te Poutama Tau students in this 2008 study were closer in ability to the national Màori-medium norm.

In the 2007 results, the top scores are off the scale and are much higher than the national Màori-medium norm (Trinick & Keegan, 2008). Notably, in both years there is no long tail of low scores in the Te Poutama Tau cohort.

**2007 2008**
**Pàngarau Scale**
**Pàngarau Scale**
*Figure 3. *Group performance of year 7 students in 2007 and 2008

**Curriculum functions report**
In number, both the 2007 and 2008 year 7 cohorts performed well above the national Màori-medium norms. However, performance in algebra was not noticeably different from the national Màori-medium norms for either cohort. As noted in the 2007 study (Trinick & Keegan, 2008), algebra seems to be an area that students ﬁ nd challenging.

**2007 2008**
*Figure 4. * Year 7 student performance in the strands of the curriculum
Te Poutama Tau Student Performance in asTTle

**Performance highlights**
**Number**
The 2008 year 7 Te Poutama Tau students in this study performed well above the national Màori-medium norms in the questions that involved recalling the basic addition/subtraction and multiplication/division facts. The Te Poutama Tau students also performed particularly well in explaining the meaning of digits in two- to three-digit whole numbers, in expressing quantities as fractions or percentages of a whole, and in ﬁ nding a fraction or percentage of a quantity. These performance highlights are also consistent with results for the year 7 Te Poutama Tau students in the 2007 study (Trinick & Keegan, 2008). A major focus is given to understanding and developing mental strategies in Te Poutama Tau to solve these types of problems, so this is a very positive outcome.

**Algebra**
The 2008 cohort of year 7 students performed slightly below the national Màori-medium norm, which is positive considering the year 4 results. The students performed well in questions linked to the learning outcomes, such as continuing sequential patterns.

**Performance concerns**
**Number**
The 2008 cohort of year 7 students had some difﬁ culty explaining the meaning of digits in numbers to two or three decimal places, writing and solving problems with decimals in multiplication and division, and using and explaining the meaning of negative numbers. The latter two areas of difﬁ culty are consistent with the 2007 results.

**Algebra**
About 50% of the 2008 year 7 cohort still had some difﬁ culty with the mathematical symbols =, <, and >. This is discussed in the following section.

The performance of the year 4 Te Poutama Tau students may be explained partly by fewer years of involvement in Te Poutama Tau. The positive performance highlights that are consistent with Te Poutama Tau include:
reading and sequencing whole and decimal numbers;
knowledge of addition and subtraction basic facts.

Some of the areas of concern for students in both the 2007 and 2008 cohorts include the use of the mathematical symbols =, <, and > and being able to describe or make up and use a rule to create a sequential pattern.
The performance of the year 7 Te Poutama Tau students in this study and in the 2007 study is very encouraging. Both cohorts performed above or close to the national Màori-medium norms. The positive results may be due to a range of variables, including teacher effectiveness or participation in other types of interventions such as literacy programmes. Notably, the majority of the year 7 Te Poutama Tau students had participated in Te Poutama Tau for a few years. The positive performance highlights that are consistent with Te Poutama Tau include:
Findings from the New Zealand Numeracy Development Projects 2008
recalling basic addition, subtraction, and multiplication facts;
reading and sequencing whole and decimal numbers.

An area of weakness for both the 2007 and 2008 cohorts were test items that involved negative numbers. This can be partly explained by the absence of material in Te Mahere Tau focusing on negative numbers. This is an area for future development. There is a similar issue with solving word problems that involve a variety of operations. Unfortunately, the asTTle test results do not reveal a student’s ability to solve problems using mental strategies, which is a feature of Te Poutama Tau.

The year 4 and year 7 groups in both years of the Te Poutama Tau/asTTle study had some difﬁ culty using the mathematical symbols =, <, and >. To learn algebra, students need a conceptual understanding of the use of symbols and the contexts in which they occur (Hiebert, Carpenter, Fennema, et al., 1997). Arcavi (1994, p. 24) introduced the notion of “symbol sense” as a “desired goal for mathematics education”. Symbol sense incorporates the ability to appreciate the power of symbols and an ability to manipulate and make sense of symbols in a range of contexts. The concept of equality, for example, is an important idea for developing algebraic concepts among learners of algebra (Carpenter, Franke, & Levi, 2003). This should be an additional area for consideration by the Te Poutama Tau facilitators in 2009 and 2010.
In summary, the 2008 year 4 Te Poutama Tau students performed below the national Màori-medium norms, while the 2008 year 7 Te Poutama Tau students mainly performed above. Why the two age groups performed differently with regard to the asTTle national Màori-medium norms is not entirely clear. However, both the 2007 and 2008 cohorts performed reasonably consistently in a number of areas, particularly in those areas that are a major component of Te Mahere Tau in Te Poutama Tau. These include number knowledge areas such as basic facts. A signiﬁ cant component of Te Poutama Tau is the development of student mental strategies to solve problems. Pencil-and-paper tests such as asTTle are limited in assessing this aspect.

Ko te kòrero whakamutunga, ko te mihi ki ngà àkonga me ngà kura i uru mai ki tènei rangahau. Nà reira, tènei te tino mihi atu ki a ràtau ko ngà pouako.

Arcavi, A. (1994). Symbol sense: Informal sense-making in formal mathematics.

*For the Learning of Mathematics, *
Carpenter, T., Franke, L., & Levi, L. (2003).

* Thinking mathematically: Integrating algebra and mathematics in elementary *
*schools.* Portsmouth, NH: Heinemann.

Christensen, I. (2003).

*An Evaluation of Te Poutama Tau 2002. * Wellington: Ministry of Education.
Hiebert, J., Carpenter, T., Fennema, E., Fuson, K., Human, P., Murray, H., et al. (1997). Making mathematics
problematic: A rejoinder to Prawat and Smith.

* Educational Researcher, 26*(2), 24–26.

Ministry of Education (1992).

* Mathematics in the New Zealand Curriculum. * Wellington: Ministry of Education.

Ministry of Education (2007a). Te Poutama Tau:

*Pukapuka tuatahi: Te Mahere Tau.* Wellington: Ministry of
Ministry of Education (2007b). Te Poutama Tau:

*Pukapuka tuarua: Te uiui aromatawai.* Wellington: Ministry of
Trinick, T., & Keegan, P. (2008). Te ara poutama: The impact of the Te Poutama Tau project on mathematics
achievement. In

*Te Poutama Tau evaluation report 2007: Research ﬁ ndings in pàngarau for years 1–10* (pp. 12–21). Wellington: Learning Media.

Trinick, T., & Stevenson, B. (2005). An evaluation of Te Poutama Tau 2004. In

*Findings from the New Zealand *
*Numeracy Development Project 2004* (pp. 56–65). Wellington: Ministry of Education.

Te Poutama Tau Student Performance in asTTle
Trinick, T., & Stevenson, B. (2006). An evaluation of Te Poutama Tau 2005. In

* Findings from the New Zealand *
*Numeracy Development Projects 2005* (pp. 34–45). Wellington: Learning Media.

Trinick, T., & Stevenson, B. (2007). Te Poutama Tau: Trends and patterns. In

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*Numeracy Development Projects 2006* (pp. 44–53). Wellington: Learning Media.
Trinick, T., & Stevenson, B. (2008). Te ara poutama: An evaluation of Te Poutama Tau 2007. In

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Source: http://nzmaths.co.nz/sites/default/files/Numeracy/References/Comp08/comp08_trinick.pdf

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