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Mathematics and StatisticsLearning Area 2012 • Scheme Y9 – 13

The following document is in three parts:-

Philosophy and SchoolOver arching vision links with school curriculum, NZC guides and links, student cohort, policies, discussions, history and knowledge, Mathematics Learning Area vision, policies and graduate profile.

Teaching, Learning Guides for Years 9, 10, 11, 12, 13VCYear guides, NCEA links, lesson guide for Years 9, 10,11, 12

Learning Area OperationsResources, structure and responsibilities. Stock take of books, calculators etc..

Appendices, Year 10, Year 11, Year 12/13, Numeracy Info.

School Mission Statement‘Success through Innovation, Determination and Courage’

“Tongariro School supports building character through cornerstone values, principles that are consistent, universal and trans-cultural which inform and direct our behaviour and attitudes.

Corner stone values build character which in turn produces behaviour that benefits the individual, and those in our community. They are the essence of healthy relationships and build a sense of community and reproduce themselves when they are practised.

The eight cornerstone values are: Honesty & truthfulness, Kindness, Consideration and concern for others, Compassion, Obedience, Responsibility, Respect, Duty”

See School Charter Documentation for more detail, clarification and interpretation. Also www.tongariro.school.nz for up to date information. This scheme and associated documents are available on this website.

2011 Demographics: Senior School:- 85% Maori students, 106 senior students, 54 boys, 52 girls.Year 10 33 studentsYear 11 33 studentsYear 12 25 studentsYear 13 15 students

Math Learning Area Interpretation and Vision

http://www.tongariro.school.nz/

http://www.nzmaths.co.nz/

Kei hopu to uringa kite aka taepa, engari kia mau kite aka matua.“Cling to the main vine, not the loose one.”

“In mathematics and statistics, students explore relationships in quantities, space, and data and learn to express these relationships in ways that help them to make sense of the world around them.” - NZC

“By studying mathematics and statistics, students develop the ability to think creatively, critically, strategically, and logically. They learn to structure and to organise, to carry out procedures flexibly and accurately, to process and communicate information, and to enjoy intellectual challenge.” –NZC

The Mathematics Learning Area considers being a multiplicative thinker as the priority need for students at Tongariro School. Such students will know and use the multiplication tables to investigate, model and solve problems. The change in the proportion of multiplicative students at every Year level will indicate the success of the mathematics department, especially in Years (7,8,9), 10. The number of NCEA Achievement with Merit/E credits will indicate the success of students at Year 11. Every credit at NCEA Level 2 or above will be considered a success.

Achieving Maori success in mathematics classrooms has a multipronged approach. These approaches include:-

Developing trusting, cooperative, respectful and informing relationships with every student. Being open minded, friendly and communicative.

Keeping a practical approach to learning new ideas foremostMaintaining learned knowledge and skillsProviding a dynamic, stimulating and informing wall displayDisplaying student and teacher generated workProviding access to high expense items such as calculatorsInvolving ICT to enhance learning situationsSupporting pathways of learning to chosen career choices

For Pasifica students and Maori students a strong relationship is developed with whanau to support the learning.

Every student will become multiplicative, a curious investigator of mathematical ideas and a willing

problem solver.

Special-needs students are attended by personal assistants and supported by other programmes within the school. These students are also welcomed into “normal” classes and learning adjusted to suit needs wherever possible and planned. Low ability students have learning adjusted to suit current ability whilst maintaining a high expectation. High ability students are encouraged to extend their learning in class time and out of class in competitions, interest groups and in discussion.

Numeracy at Tongariro School – The SituationMore data needs to be collected and interrogated. However one year of employment has allowed some insights and deductions to be made. The numeracy data from previous years, the current data all need to be tabled for use across the school. [See ERO report 2011] . Data unavailable at Dec 12 2011.

The literacy levels of the students are likewise very low compared to national expectations. A fairer statement might be that the variation within the student cohort is wide in both numeracy and literacy with a general guide that the students are about a year or so behind expectation. Some are more and some are less, behind. The reasons for this are many, some known, many unknown.

In the mathematics classroom therefore:-- the reading of questions out loud is encouraged- the drawing of the problem asked is demanded- the logical development of the strategy used talked about- the recording of the solution using logical mathematics statements is

expected- the writing of the answer to the question asked with full sentence

structure demanded- reasons given for all steps in a recorded solution- each problem solved is critically reviewed - posters of projects are developed and presented- career paths are monitored- ICT is used where ever appropriate-

In this way literacy is developed in the context of Mathematics and Statistics.

What is success? This question needs to be answered by the Minister, the Principal and teachers alike. The interpretation in mathematics is measured by the proportion of multiplicative students at any school level, as mentioned above. Another measure is the number of CL6 passes (Merit or E at NCEA L1), and another is the number of NCEA L2 passes (which measures CL7 performance). In this school success could be the percentage of students whose attendance is over 80% for any period of time or the percentage of students who gain NCEA L1. The Minister has suggested that success is gaining NCEA L2. Only 20% of any cohort get to study successfully at CL7 (Y12) [See historical School Cert, NCEA data on www.nzqa.govt.nz].

http://www.nzqa.govt.nz/

Level Structure at Tongariro School and Other FactorsTongariro is an Area school. It is not “one” school. It is currently three schools operating on the same campus. The Principal has more of an advisory role and three DP’s oversee the organization and daily running of the primary, intermediate and senior schools. The intermediate school comprises Year 7, 8 and 9 students. Some senior teachers take intermediate classes mainly in technology. Specialist extension classes are not promoted yet.

Further investigation shows a lot of copied sheet work with no set text or programme of work, some note copying from the white board and a class structure resembling Year 8 homeroom style rather than a more tradition Year 9 class where students move to another class. The current Year 9 students do not get a lot of testing, extension, or problem solving and it is likely that as has been identified by the Ministry, most of the Intermediate teachers have little mathematical knowledge beyond CL3 [See Numeracy Research Reports on www.nzmaths.co.nz]

Year 10 is a bridging year between a class based learning environment of Middle School Y7 to 9 and the senior school approach of moving students to specialist classroom teachers. The mathematics programme encourages all aspects of the key competencies but stresses mathematical thinking and communication. From 2012 this year group will be called PNCEA meaning Pre-NCEA so that the focus is clearly identified for future success.

During 2011 there were two teachers of mathematics in the Senior school. There were three classes in Year 10 2010, usually 2, 2 classes of Year 11, 2 classes of Year 12 and a couple of Year 13 students using VC but with a tutor for 5 periods a week. In 29012 there is a Year 9, 2x Year 10, 2x Year 11, 3 x Year 12.

The department is well resourced with texts, calculators, data-show and computers. In 2011 Year 10 students have 4 timetabled 45 minute math classes or 3.75hrs if they are on time and on task and stay the whole period. Year 11 and 12 students have 5 timetable 45minute periods. In Year 2012 current plans are that Year 9 will have three hours per week, Year 10 three hours per week, Year 11m 12 four hours per week.

The school absenteeism rate is about 20 to 30% overall with much variation. Late to school is a common event and taking days off is common. In Year 10 the median is 74% present, half of the students are present between 60% and 81% of the year, the least is 30% attendance and the most 97%. This single event causes learning difficulties that are unsustainable.

Mathematics is learned sequentially and progresses from one lesson to the next with each building on the one before. Absence from class creates a gap in learning and consequent delay, sluggish performance, frustration, behavior problems and increase in teacher workload. A key priority for this school must be to get students to school, on time, ready to learn. [See ERO report 2011].


From classroom observation in 2010 many students are reluctant learners, undisciplined and not used to doing homework, study or investigation. A general description might be they have not yet learned how to learn.

Every effort is made to normalize homework and assignment expectations. It has been suggested that identified students with learning reluctance or lack of learning skills be withdrawn for a day or two of intense direction to remedy these issues and then constantly monitored. Increasing student achievement, (and in this school that means Maori success) will then be accelerated to more acceptable levels. The community, parents would need to be involved and made active participants in this process as well.

Implications for Mathematics Programmes Year 9 to 13, 2012.Statistics requires literacy so this subject has to be introduced in a practical way and developed along with the literacy required. The students are quite visual and kinesthetic learners. Shape and geometry is a natural avenue for learning so these topics form the central theme of year programmes. Through geometry number, algebra, measurement and probability and statistics are discovered. This may well imply that statistics is not a core subject for students until they have sufficient literacy to support the learning.

The NCEA L1 award realistically will be a two year goal for 50% of the students.

All students will eventually gain numeracy over 2 years.

A practical component for mathematics and a context in which mathematics can be studied will be trialed in 2012. There are some Level NCEA Physics standards that offer a good reason to know about measurement and measure in a real context. These papers will be combined with the mathematics standards selected to make a course.

There will be two main courses at Level 1 with a Work and Study Skills Fallback.

App Mat 1 will be a faster pace for the better students, offer 24cr and will use a selection of achievement standards including one from Physics. Students in App Mat 1 will be expected to gain numeracy requirement for NCEAL 1 from Achievement Standards.

Mat 2 will be a selection of the easier standards and offer about 20cr at a slower pace. Students failing to show a convincing and sufficient ability that they will gain numeracy for NCEA through Achievement standards will be guided toward the Work and Study Skills standards, see below.

There is also a third option for very low achieving students. Identified students will be asked to complete the Work and Study Skills unit standards through which 10 numeracy credits gained will satisfy the NCEA L1 numeracy requirement.

Courses that follow are :- Year 9, Year 10, Y11 Work and Study Skills, Year 11 Applied Mat 1, Year 11 Mat 2, Year 12 Mathematics, Year 12 Statistics. The Year 13 courses are studied using VC and are not included.

All Course Guides • 2012

Overview

All Courses in Mathematics and Statistics for 2012. This section parts are copied for the senior course selection books.

Kei hoputouringakite aka taepa, engarikiamaukite aka matua.“Cling to the main vine, not the loose one.” -NZC

All achievement objectives in Year 11 NCEA courses are at Curriculum Level 5 or 6. All assessment in Year 12 is at Curriculum Level 7 and in Year 13 at Curriculum Level 8. These are huge jumps in learning progression. Demonstrating one has the ability to study at a higher level is by gaining 8 Merit or Excellence credits. For example, to study at Year 12, 8 Merit credits are needed from any mathematics standards in Year 11.

The Numeracy Unit Standards are owned by the Work and Study Skills area of NZQA and are not mathematics standards for that reason. These unit standards are suitable to gain the minimum needed to satisfy the numeracy NCEA Level 1 requirement. They are internally assessed and are set mostly at Curriculum Level 4. They are not a suitable requirement for progression past CL5.

Most Year 11 students are expected to gain numeracy through the Achievement Standards over a period of 1 or 2 years depending upon ability. A small group of students will need to use the Work and Study Skills Numeracy Standards and use a portfolio of evidence collected from across their subjects to gain the NCEA L1 numeracy requirement. [see www.nzqa.govt.nz for all updates].

Problem solving and extension of mathematical thinking are a priority of the mathematics department. Creating a curiosity in mathematics to explore the myriad of patterns and mysteries in number is a serious aspect of learning mathematics. Being able to reason, explain and prove why things are, enables an understanding of the real world that opens doors of opportunity and develops and enduring and lifelong quest for truth and honesty.

Mathematics is a human endeavor that can develop into careers in technology, physics, meteorology, geophysics, business, science and engineering.

http://www.nzqa.govt.nz/

Years7, 8 and 9 Mathematics and Statistics

The senior school has minimal input into this program but dialogue with senior managers of the Middle School involved connections to expectations. This department is content with the existing program at Year 7, 8 and 9 which has number as the key focus. It is suggested that extension classes for small groups of between 10 and 15 students of similar ability are involved with investigative mathematics and problem solving to enhance the existing Year 7, 8, 9 programs as these skills need developing. The other strands are going to be enhanced through existing programs in 2012 while maintaining the focus on number to Level 4 and 5 in NZC. Mathematics has to be an enjoyable activity for students. A quiz event and display during mathematics week, or thereabouts is a planned annual event. Data from Year 9 is shared with this department.

See above for some relevant comments and observations from 2011 about the current Year 10 Mathematics instruction. (Note Year 9 class for 2012).

Focus concepts, knowledge and skills that can be enhanced in Years 7 to 9 include

- using multiplication to solve problems and using times tables- drawing a set of axes to plot simple linear graphs- elementary algebra of continuing simple patterns- elementary algebra of solving by guess and check- know the names of basic geometrical triangles, quadrilaterials and

symmetrical polygons- use isometries and enlrgement- Can describe a pattern in numbers using nth term ideas- Knows 8 points of the compass- Knows 10 facts of basic geometry of straight lines and triangles.- Can use a broken ruler to measure within and without the size- Knows units for mass, time, capacity, area.- Can use a chance tool such as a die or coin to play a game.- Has a working knowledge of the PPDAC investigative cycle- Has investigated 3 questions on Census at Schools website - Has completed a personal careers pathway investigation (see below)- Has completed 3 investigations into a mathematical idea, person or

problem.

This list needs to be reviewed and amended accordingly as identified needs and issues arise. This could be done along with the formal development of a mathematics programme for these years.

Year 9 Mathematics and Statistics

Overview and Student Guide

The aim of the mathematics department is to cultivate a curiosity of mathematics in every student and for each to become a problem solver. Mathematics is not just a set of skills or rules that is to be learned; it is a connected way of thinking.

Mathematical thinking is about being logical, strategic, creative and critical. Problem solving and investigation are emphasized and opportunities to take part in regional and international competitions are offered..There are 6 main strands:• Number – Understanding and using multiplication and proportional thinking to solve problems• Algebra – Developing skills and algebraic thinking.• Measurement – Practical measuring and estimating to solve problems• Geometry – Exploring and explaining the properties of shapes• Statistics – PPDAC cycle of investigative statistics• Probability – Exploring chance and variation

AssessmentStudents will complete an AsTTLe test during the year to measure progress against the NZC Levels 3, 4, 5 in Number, Geometry and Algebra. Everyone’s Numeracy Stage will be monitored.

There will be a presentation of an investigation during the year.

DurationA full year programme

Course PrerequisiteSuccessful completion of a Year 8 Course.

Course Fee $12Stationery Required1 x 1J8 Quad bookCASIO fx82AU (optional)Pens, pencil, ruler, eraserDragon Homework Book ($12)

Future PathYear 10 Mathematics

Year 9 Unit 9 Guide • Summary, see Unit Guides in File Box for details.

Term 1Number (3 weeks)Measurement (3 weeks)Statistics (3 weeks approx)CL3/4/53 topic tests, multiplication tables checks as required, EOTerm Com Test.

Number concerns place value, squares, square roots, number patterns.Measurement is about the SI units, practical measuring and calculation.Statistics is about the PPDAC, doing a survey, dot plots and box/whisker

Term 2Trigonometry (3 weeks)Geometry (3 weeks)Algebra (3 weeks approx)CL3/4/53 topic tests, multiplication tables checks as required, EOTerm Com Test.

Trigonometry Scale drawing and enlargement.Geometry revises triangles, quad, constructions, simple proofs.Algebra extends the number, patterning, and simple solving, substitution, manipulation skills.

Term 3Percentage (3 weeks)Transformations (3 weeks)Probability (3 weeks approx)CL3/4/53 topic tests, multiplication tables checks as required, EOTerm Com Test.

Percentage change, increase and decrease. Level 5 problems.Transformations is about reflections, rotations and translations.Probabilty in a practical sense, experimental and simlulation.

Term 1Algebra (3 weeks)Revision (3 weeks)Model Making (2weeks)CL3/4/53 topic tests, multiplication tables checks as required, EOYear Com Test.

Algebra manipulation and solving. More complex and word problems.Revision of year for examinations.Model making of stellated platonic solids.

Note, Numeracy is a whole year, every day event and is used to introduce the day or lesson. Homework focuses on previous learning and practicing new skills.

Puzzles and problems, Australian Math Comp problems, BOPMA problems and the like from “Broken Calc”, Starter of the Day used every day. Problem solving is pushed as a puzzle skill for enjoyment.

Every student must also produce a project and present this to the class during the year. This is likely to be a poster, problem solved, model etc.

See Year 9 Guide Mathematics

P-NCEA (Y10) Mathematics and Statistics

Overview and Student Guide

The aim of the mathematics department is to cultivate a curiosity of mathematics in every student and for each to become a problem solver. Mathematics is not just a set of skills or rules that is to be learned; it is a connected way of thinking.

Mathematical thinking is about being logical, strategic, creative and critical. Problem solving and investigation are emphasized and opportunities to take part in regional and international competitions are offered..There are 6 main strands:• Number – Understanding and using multiplication and proportional thinking to solve problems• Algebra – Developing algebra skills and algebraic thinking.• Measurement – Practical measuring and estimating to solve problems• Geometry – Exploring and explaining the properties of shapes• Statistics – PPDAC cycle of investigative statistics• Probability – Exploring chance and variation

AssessmentStudents will complete an AsTTLe test during the year to measure progress against the NZC Levels 3, 4 and 5 in Number, Geometry and Algebra. Everyone’s Numeracy Stage will be monitored.

There will be a presentation of an investigation during the year.

DurationA full year programme

Course PrerequisiteSuccessful completion of a Year 9 Course.

Course Fee $12Stationery Required1 x 1J8 Quad bookCASIO fx82AU (optional)Pens, pencil, ruler, eraserDragon Homework Book ($12)

Future Path

NCEA L1 Mathematics 1, either Mat 1 or Mat 2

Year 10 Guide • Summary, see Unit Guides in File Box for Year 10.

Term 1Number (3 weeks)Measurement (3 weeks)Statistics (3 weeks approx)CL 4/53 topic tests, multiplication tables checks as required, EOTerm Com Test.

Number concerns ratio and proportion.Measurement is about the SI units, practical measuring and calculation.Statistics is about the PPDAC, doing a survey, dot plots and box/whisker, making an informal inference.

Term 2Trigonometry (3 weeks)Geometry (3 weeks)Algebra (3 weeks approx)CL 4/53 topic tests, multiplication tables checks as required, EOTerm Com Test.

Trigonometry introduces sine, cosine and tangent ratio, Pythagorus.Geometry revises triangles, quad, constructions, simple proofs.Algebra extends the number, patterning, and simple solving, substitution, manipulation skills.

Term 3Percentage (3 weeks)Graphing (3 weeks)Probability (3 weeks approx)CL 4/53 topic tests, multiplication tables checks as required, EOTerm Com Test.

Percentage change, increase and decrease. Level 5 problems.Graphing is of linear relations, gradient and intercept, a parabola.Probabilty in a practical sense, experimental and simlulation.

Term 1Algebra (3 weeks)Revision (3 weeks)Model Making (2weeks)CL 4/53 topic tests, multiplication tables checks as required, EOYear Com Test.

Algebra manipulation and solving. More complex and word problems.Revision of year for examinations.Model making of stellated platonic solids.

Note, Numeracy is a whole year, every day event and is used to introduce the day or lesson. Homework focuses on previous learning and practicing new skills.

Puzzles and problems, Australian Math Comp problems, BOPMA problems and the like from “Broken Calc”, Starter of the Day used every day. Problem solving is pushed as a puzzle skill for enjoyment.

Every student must also produce a project and present this to the class during the year. This is likely to be a poster, problem solved, model etc.

NCEA L1 Applied Mathematics • AP 1

Overview

This course is designed for all students who have a continuing interest in mathematics or plan on a career involving more advanced mathematics and statistics. Students studying a science, technology or business should also be studying mathematics. Students are expected to complete this course with at least 16 credits with 8 being Merit so that entry to the Year 12 Mat 1 course is guaranteed. The Math 1 is registered with NZQA and students sufficient Merit or above credits can gain course distinction. Three Physics standards are offered and success could lead to a Physics course at Year 12.

NZQA Registered Mathematics – Applied Mathematics 1 (24cr)AS91026 – Apply number reasoning in solving problems (4cr)AS91027 – Apply algebraic procedures in solving problems (4cr) EXT CAT AS92029 – Apply linear algebra in solving problems (2cr)AS91031 – Apply geometric reasoning in solving problems (4cr) EXTAS91032 – Apply right-angled triangles in solving measurement problems (3cr)AS91036 – Investigate bivariate numerical data PPDAC, statistics (3cr)AS90935 – Carry out a practical physics investigation, linear (4cr)

In addition these achievement standards may be assessed if appropriate as content from these standards has been taught in previous years and may be revised and extended within this course as appropriate.AS91028 – Investigate relationships between tables, eqns and graphs (4cr EXT)AS91030 – Apply measurement in solving problems (4cr)AS91033 – Apply knowledge of geo reps in solving problems (3cr)AS91034 – Apply transformational geo in solving problems (2cr)AS91035 – Investigate a given multivariate data PPDAC (4cr)(4cr literacy)AS91037 – Demonstrate understanding of chance and data (4cr) EXTAS 91038 – Investigate a situation involving elements of chance (3cr)(3cr literacy)AS90940 – Demonstrate understanding of aspects of mechanics. (4cr EXT)AS90938 – Demonstrate understanding of aspects of elec and mag (4cr EXT)AS90936 – Demonstrate understanding of the physics of an application (2cr)(3cr literacy)

Numeracy is expected to be gained through success in Achievement Standards.

Students are expected to sit at least one external achievement standard and the Common Assessment Task (CAT) in Algebra. A selection of internal achievement standards will also be assessed. Total credits offered exceeds 20 and will be dependent upon student cohort. See the Course Guide for further details.

Course Completion requires 85% attendance to classes. Official school events such as Athletics and Swimming Sports are not absences but any other absence where normal class cannot be suspended is an absence. Absence includes truancy, sickness, tangi, sporting events for example. 15% absence from 36x4 is 21 hours of class time. It is the student’s responsibility to catch up with notes and problems after being absent.

AssessmentDaily and weekly informal assessment drives the lesson progression. Internal assessments follow learning for that topic. The CAT is expected on 21st September. The external examinations begin in early November.

Homework, Workbooks and Exercise books.Students are expected to develop work habits that will be beneficial in following years. These include keeping a tidy exercise book of classroom notes and exercises, completing a workbook of revision of previous years, establishing a habit of regular homework, assignments and becoming a problem solver.

DurationThis is a full year course and is considered to be of 140hrs duration or 180 45minutes periods.

Extension and Challenge OpportunitiesAustralian Mathematics Competition, National Bank Senior Competition

Course Fee$20 is expected as payment for the homework write-in book. $20 may be required for a Physics write in book for interested students.

Stationery RequiredA mathematics quad book, coloured pencils, pencil, biro, ruler and compass. CASIO fx82AU. A physics quad book may be required for interested students.

Future PathYear 12 Mathematics • Mat 1 with 8 Merit credits from this course.Year 12 Physics • Physics 1

NCEA L1 Mathematics 2

Overview

This course is designed for all students who have not found learning mathematics an easy task but do require mathematics and statistics in their choice of career. The mastering of reasoning with number, measurement and geometry is emphasized with other strands of algebra, statistics and probability introduced and developed at an appropriate rate. Students are expected to gain numeracy for NCEA Level 1 award and at least 16 credits over a two year period.

NZQA Registered Mathematics • Mat 2 (24cr)AS92029 – Apply linear algebra in solving problems (2cr)Unit Standard 5223(1cr)AS91030 – Apply measurement in solving problems (4cr)Unit Standard 26567(2cr)AS91032 – Apply right-angled triangles in solving measurement problems (3cr)Unit Standard 5236(1cr)AS91033 – Apply transformation geometry in solving problems (3cr)AS91034 – Apply transformational geometry in solving problems (2cr)AS91036 – Investigate bivariate numerical data using PPDAC (3cr)(3cr literacy)AS91038 – Investigate a situation involving elements of chance (3cr)(3cr literacy)

In addition these achievement standards may be assessed if appropriate as content from these standards has been taught in previous years and may be revised and extended within this course as appropriate.AS91026 – Apply number reasoning in solving problems (4cr)AS91027 – Apply algebraic procedures in solving problems (4cr) EXT CAT AS91031 – Apply geometric reasoning in solving problems (4cr) EXTAS90935 – Carry out a practical physics investigation, linear (4cr)

Numeracy is expected to be gained through success in Achievement Standards over a two year period however students not gaining numeracy sufficiency may be directed to focus on gaining the Numeracy Unit Standards with input from other subject areas. (10cr).

AssessmentDaily and weekly informal assessment drives the lesson progression.

Course Completion requires 85% attendance to classes. Official school events such as Athletics and Swimming Sports are not absences but any other absence where normal class cannot be suspended is an absence. Absence includes truancy, sickness, tangi, MPA, sporting events for example. 15% absence

amounts to a generous 27periods or 21 hours of class time. It is the student’s responsibility to catch up with notes and problems after being absent.

Homework, Workbooks and Exercise books.Students are expected to develop work habits that will be beneficial in following years. These include keeping a tidy exercise book of classroom notes and exercises, completing a workbook of revision of previous years, establishing a habit of regular homework and becoming a curious problem solver.

DurationThis is a full year course and is considered to be of 140hrs duration or 180 45minutes periods. Students may repeat this course to gain the required credits in the following year.

Course Fee$20 is expected as payment for the homework write-in book.

Stationery RequiredA mathematics quad book, coloured pencils, pencil, biro, ruler and compass. CASIO fx82AU

Future PathYear 11 Mathematics • App Mat 1 with any 12 credits from this course.Year 12 Mathematics • Mat 1 or 2 with 16 credits with 8 being Merit credits from this course.

NCEA L1 Numeracy Course

Overview

This course is designed for students who need to gain numeracy and are identified as having learning difficulties. Students will have been identified at CL2 or 3 and other mathematics courses at this level are inappropriate to undertake. Entry to this course is only with the permission of the HOD Mathematics.

A variation of this course is offered in 2012 to support low achieving students needing the numeracy requirement for NCEA L1.

TopicsThe following Unit Standards will be available:-26623 Use number to solve problems (4cr)26627 Use measurement to solve problems (3cr)26626 Interpret statistical information for a purpose (3cr)In addition there may be applied mathematics investigations and activities including the NZAMT MAP programme.

AssessmentThe three unit standards above are internally assessed and have no examination content. The Unit Standards 5223(1cr), 5236(1cr) and 26567(2cr) may be assessed depending upon need and demand. The MAP programme is internally assessed and organized by NZAMT (www.nzamt.org.nz).


DurationThis is a one semester course. Failure to complete numeracy allows access to the second semester to repeat the opportunity. There is no course completion requirement relating to absence.

Course Fee$10 is expected as payment for the MAP Course and Certificate.CASIO fx82AU

Stationery RequiredA mathematics quad book, coloured pencils, pencil, biro, ruler and compass. Future PathYear 11 Mathematics • Course 2 after NCEA numeracy requirement is gained. Entry to this course is only with the HODS Mathematics permission.

NCEA L1 Practical Physics

Overview, not offered 20112.

This course is a one year course designed to support students who prefer to learn mathematics and physical science through practical study and experimentation. Expected outcomes for the course include gaining some physics credits at NCEA Level 1 in experimentation, mechanics and electricity.

TopicsThe following Achievement Stands will be available:-AS90935 Carry out a practical physics investigation (4cr) INTAS90936 Project (2cr) INT(2cr literacy)AS90937 Electricity and magnetism (4cr) EXTAS90939 Heat (4cr) EXTAS91035 Investigate bivariate numeraical data using PPDAC (3cr)

Numeracy (10cr needed)can be gained through success in the achievement standards assessed in this course.



Course Completion requires 85% attendance to classes. Official school events such as Athletics and Swimming Sports are not absences but any other absence where normal class can not be suspended is an absence. Absence includes truancy, sickness, tangi, MPA, sporting events for example. 15% absence amounts to a generous 27periods or 21 hours of class time. It is the students responsibility to catch up with notes and problems after being absent.


Stationery RequiredA mathematics quad book, coloured pencils, pencil, biro, ruler and compass. CASIO fx82AUFuture Path

NCEA L2 Physics

NCEA L2 Mathematics • Mat 1

Overview

This course is designed for all students who have a career plan that includes further study at a technical institute or university to undertake a course in engineering, science, or technology. Mathematical thinking becomes quite demanding at this level, includes intense algebra and calculus development and entry is approved only with permission of the HOD Mathematics. As a guide a minimum of 8 Merit credits in the Year 11 MP1 course is required for entry.

NZQA Registered L2 Mathematics • Mat 1 (23cr)AS91256 – Apply coordinate geometry methods in solving problems (2cr)AS91257 – Apply graphical models in solving problems (4cr) AS 91258 – Apply sequences and series in solving problems (2cr)AS 91259 – Apply trigonometric relationships in solving problems (3cr) AS 91261 – Apply algebraic methods in solving problems (5cr EXT)AS 91262 – Apply calculus methods in solving problems (5cr EXT)AS 91268 – Investigate a situation using a simulation (2cr) (2cr lit L1.)Students are expected to sit both external achievement standards.

AssessmentDaily and weekly informal assessment drives the lesson progression. Internal assessments follow learning for that topic. The external examinations begin in early November. Assignments are a required aspect of course completion.


Course Completion requires 85% attendance to classes. Official school events such as Athletics and Swimming Sports are not absences but any other absence where normal class can not be suspended is an absence. Absence includes truancy, sickness, tangi, MPA, sporting events for example. 15% absence amounts to a generous 27periods or 21 hours of class time. It is the students responsibility to catch up with notes and problems after being absent.


Stationery RequiredA mathematics quad book, coloured pencils, pencil, biro, ruler and compass. CASIO fx82AUFuture PathYear 13 Mathematics • Calculus with 8 Merit credits from this course.

Year 13 Mathematics • Statistics with 8 Merit credits from this course.

NCEA L2 Statistics • Stat 1

Overview

This course is designed for all students who intend to undertake study at tertiary or university level with mathematics as a support subject and statistics as a requirement for entry. This course does not include the formal development of algebra or calculus and is suitable for science, social science and students of mathematics. This course is about statistics and probability.

NZQA L2 Statistics • Stat 1 (20cr)AS 91260 – Use networks in solving problems (2cr)AS 91263 – Design a questionnaire (3cr) (lit)AS 91264 – Use statistical methods to make an inference (4cr) (lit)AS 91265 – Conduct an experiment to investigate a situation using statistical methods (3cr) (lit)AS 91266 – Evaluate a statistically based report (2cr)( (lit)AS 91267 – Apply probability methods in solving problems (4cr EXT)(lit)AS 91268 – Investigate a situation using a simulation (2cr) (lit)

Students are expected to sit the external achievement standard.

AssessmentDaily and weekly informal assessment drives the lesson progression. Internal assessments follow learning for that topic. The external examinations begin in early November. Assignments are a required aspect of course completion.

Course Completion requires 80% attendance to classes. Official school events such as Athletics and Swimming Sports are not absences but any other absence where normal class can not be suspended is an absence. Absence includes truancy, sickness, tangi, MPA, sporting events for example. 15% absence amounts to a generous 27periods or 21 hours of class time.



Stationery RequiredA mathematics quad book, coloured pencils, pencil, biro, ruler and compass. CASIO fx82AUFuture PathYear 13 Mathematics • Statistics with permission of HOD.

NCEA L2 Physics

Overview • not available 2012

This course is a one semester course designed to support students who prefer to learn mathematics and physical science through practical study and experimentation. Expected outcomes for the course include gaining some physics credits at NCEA Level 2 in experimentation, mechanics and waves including light. This course does not aim to cover all aspects of the physics at this level but a sufficiency to allow sensible choice at Year 13 for a successful student.

TopicsThe following Achievement Stands will be available:-AS 2.1 Practical Investigation (4cr) INTAS2.2 Practical Application (3cr) INTAnd choice of either of the following (due to time restriction)AS2.6 Practical electricity, electronics and magnetism (not assessed)AS 2.4 Physics of waves (4cr) EXT

Numeracy contributing to NCEA L1 (10cr)can be gained through success in the achievement standards assessed in this course.


DurationThis is a one semester course.


Stationery RequiredA mathematics quad book, coloured pencils, pencil, biro, ruler and compass.CASIO fx82AU

Future PathNCEA L2 Physics (complete course by VC)NCEA L3 Physics Engineering, Science and Technology, medicine, business.

NCEA L3 Mathematics • Calculus


This course is designed for students who enjoy mathematics or plan to pursue an engineering or related course. Students undertaking this course are expected to be self-motivated and keen to achieve.

TopicsCalculus, trigonometry, complex algebra and advanced geometry.

Students are expected to sit all external achievement standards. All internal achievement standards will also be assessed. Total possible credits 20+.

AssessmentDaily and weekly informal assessment drives the lesson progression. Internal assessments follow learning for that topic. The external examinations begin in early November. See Course Guide for further details.

DurationThis is a full year course or two semester course.


Stationery RequiredA mathematics quad book, coloured pencils, pencil, biro, ruler and compass. CASIO 9750G-Plus

Future PathTertiary institution for engineering, physics, mathematics, business. See careers websites for specific information.

NCEA L3 Mathematics • Statistics


This course is designed for students who enjoy mathematics or plan to pursue a career in science or social science. Students undertaking this course are expected to be self-motivated and keen to achieve. Students undertaking the L3 Calculus course would be likely to take this course as well.

TopicsStatistical methods involved with time series data, bivariate data, modeling, experimental design, probability distributions and linear systems.

Students are expected to sit all external achievement standards. All internal achievement standards will also be assessed. Total possible credits 20+.

AssessmentDaily and weekly informal assessment drives the lesson progression. Internal assessments follow learning for that topic. The external examinations begin in early November. See Course Guide for further details.

DurationThis is a full year course or two semester course.


Stationery RequiredA mathematics quad book, coloured pencils, pencil, biro, ruler and compass.

Future PathUniversity for engineering, physics, mathematics, business, science, social science, statistics. See careers websites for specific information.

NCEA L3 Physics • VC


This course is a full year VC course covering and assessing all aspects of physics at this level. Experimentation and learning support is supplemented within the school environment.

TopicsThe following Achievement Stands will be available:-AS91026 – Apply number reasoning in solving problems (4cr)

Numeracy (10cr)can be gained through success in the achievement standards assessed in this course.


DurationThis is a one semester course.


Stationery RequiredA mathematics quad book, coloured pencils, pencil, biro, ruler and compass.

Future PathNCEA L2 Physics

INDIVIDUAL LEARNING PLAN (ILP)

All students in the senior school with co-develop an ILP to cater for their own needs and aspirations. The courses at each level are sufficiently flexible to cater for most variations.

See ILP resource in Math Folder.

The ILP will include:-- career studies- pathway planning with Year 10, 11, 12, 13 connections- achievement record to date in mathematics and literacy- a monitoring reflective journal by the student and the teacher.- short term and longer term goals.

Career Pathway Investigation General

This guide is for use by students at Year 7 to 13. It is expected that this unit will be completed at least three times per year or once per term. The information is presented once per year to the whole class by each student as part of the development of public speaking and presentation. These studies are collated in the ILP folder.

Se Career Unit resource in Math Folder.

Departmental Operations

The mathematics department consists of two teachers operating in Room 22 and 21. There is no HOD office as such and all NCEA student information are stored in the white cabinet in Room 22.

The resource room contains a wide range of texts, teacher reference and mathematics equipment. The calculator of choice is the CASIO fx-82AU plus at all levels. Students in Year 12 and 13 may also use the set of Casio 9895 graphics calculators for more indepth work. Computers are available with graphing software and fathom for Statistical work.

Every room has a data show and these are used to enhance teaching events. Sites include NZAMT, NZQA, NLVM and Myphysicslab.com.

A more complete list of websites is planned. Likewise a complete stocktake of the mathematics department as time permits.

ResponsibilitiesHOD

- Everything- NCEA records- Academic Courses.

Ass HOD/DEAN- Every thing else- Sanity of the HOD- MAP courses

Appendix 1 • Year 10 Analysis 2011

Data for the Year 10 students 2010 was provided by the school. This data was incomplete and not at all summarised. The data did show that of the Year 10 cohort 2010, a few, 5% were still Counters (CL1), 20% or so were Early Adders (CL2), the majority 65% Advanced Adders (CL3) and a small 10% Multiplicative (CL4) or better, Proportional thinkers.

Year 10 Cohort Nov-10 Nov-11 Nat DataStage 4 5% 0% 2%Stage 5 20% 2% 12%Stage 6 65% 52% 25% Stage 7 10% 26% 40%Stage 8 0% 21% 21%

The success is the increase in Stage 7/8 or 37%, or 37/10 =370% increase. The average stage gain was 0.8 (s= 0.6) with some students making zero gain and 3 students making a gain of 2 stages during the year. AssTTLe research states a 0.66 gain is the normal for an average student who attends school. [see AssTTLe research data Fiona Ells]. The cohort made good progress overall but 8 students made no measureable gain. It must be stated that each numeracy stage is wide and students can move within a stage, make progress and not be noticed.

Further analysis comparing stage change with attendance rate shows students present 80% of the year often gained 2 stages but the correlation showing being present is better for progress is quite varied and complicated by other factors. Those making no gain were also absent over half of the year as might be expected. (xxxmight be an idea to create this as an appendix and repeat for Year 10,11,12)

Nov-10 Nov-11 Nat Data0%

10%

20%

30%

40%

50%

60%

70%

Stage 4Stage 5Stage 6 Stage 7Stage 8

The Year 10 cohort started a about a year behind expectation and about two years behind national expectation and all but 10% failed to achieve the National Standard for Year 8 students. [This statement needs to be examined yearly for each cohort.] In Nov 2011 this cohort had changed and become more multiplicative and ready for NCEA L1. The national data also over estimates the top end performance is now of a similar shape to these students showing that they have largely caught up. The Stage 6 adders/early multipliers are still over represented but typical of most secondary cohorts in other schools.

The prediction for 2012 NCEA L1 Mathematics performance is the 20% (8) Stage 8 students become Merit and Excellence passes and will easily cope with Year 12 mathematics the following year. The 10 Stage 7 students will gain NCEA L1 Mathematics and then take 2 years to gain the NCEA L2 Mathematics. The 20 Stage 6 students will take 2 years to gain sufficient NCEA L1 mathematics credits but will gain numeracy through achievement standards. The few Stage 5 students will need to use the Work and Study Skills Numeracy Unit Standards to gain the numeracy component of NCEA L1 and will otherwise find mathematics a very difficult subject in which to gain credits. A special accelerate programme for these students is advised if success is to be measured by NCEA.

Appendix 2 • Year 11 Analysis 2011

The Year 11 cohort was a diverse group of learners. There was a significantly large group who had low numeracy and were operating at CL 4 or below. The data shows that while the NCEA numeracy requirement was near 100% the reliance upon Unit Standards below number 5232 (below CL5 or Group B) was heavy. This data excludes External results unavailable at the time of writing.

Year 11 Cohort 2011* 2010* 2009*Total 580 405 386US 515 389 343CL5 437 329 316CL6 78 60 27AS 65 16 43ME 19 4 5

Total US CL5 CL6 AS ME0

100

200

300

400

500

600

700

2011*2010*2009*

There was a significant increase in success using the new Achievement Standards and a huge improvement (450%) in the awarding of Merit and Excellence grades. Of the cohort of 39 students 6 gained the pre-requisite for entry to Year 12 mathematics. The external results not available at the time of writing may change this statistic. [The requirement is 8 Merit or better credits, CL 6 or better or with permission of the HOD].

The problem of what to do with a large group (36) returning Year 11 students who need to establish a mathematics platform at Year 11 and the incoming Year 10 students, another 39, implies 3 classes will have to be available for this large group. The general low achievement caused by lack of readiness for learning and absence creates this bottleneck and remains the most significant problem facing the school. Management are aware of this issue.

One possibility, like Year 12, see below, is to create a Year 11 Statistics focus course or low algebra option. There are 12 credits and 6 in geometry that could form an alternative Year 11 course for returning students. The pathway to Year 12 is then also statistics and that course is available in 2012 as well for returning Year 12 students, see below.

Appendix 3 • Year 12/13 Analysis 2011

The Year 12 students were a very diverse group of learners and included Year 13 students who were unprepared for CL 8 mathematics and statistics standards. February analysis showed 2 credits at CL 6 and 31 credits at CL 5 for the complete group indicating a very unprepared group and pending difficulties. The group achieved 65 US Level 1 credits during the year and 19 M/E passes in Level 1 Achievement Standards. The external results were unavailable at the time of writing and may affect the results. Many of the passes were at NCEA L1 however.

One student gained 5 L2 credits and sat the final examinations.

This group will be guided to a low algebra statistics course on return in 2012 if possible.

The year 13 students were 2 very amazing, self managed students who excelled and will easily gain NCEA 3, probably with distinction. Both are intending to enroll in undergrad degrees at Waikato University in 2012.

Appendix 4 • Numeracy Journey

The Numeracy Learning JourneyRefer to www.nzmaths.co.nz for all resources, supporting documents, reports and research papers concerned with the NZ Numeracy Project which was implemented throughout NZ schools 1998 to 2011. The project created a language for mathematics teachers of primary, intermediate and secondary to communicate effectively about the mathematical thinking being done by students. The research based project established that students proceed through a simple 1 to 1 counting, adding, advanced adding, multiplying and to proportional thinking stages, all of which are heavily reliant on place value understanding. These ideas are strongly represented in this scheme.

A Brief History of the NZ Numeracy ProjectThe beginnings stem from noticing a steady decline in computational skills in students and young adults during the 1980’s and 1990’s. The SIMMS study, and later the TIMMS study confirmed the trend and alerted the Ministry of Education to resource an intervention. The Count Me In Two project and the UK Numeracy Project both informed consequent planning in NZ and the NZ Numeracy Project was created.

Pilot projects followed in 1999, 2000 and 2001 in primary, intermediate and secondary schools. The ENP (Early Numeracy Project) was then prioritized, two years later the ANP (Advanced Numeracy Project) was likewise released to build on the ENP, then the INP (Intermediate Numeracy Project) was started in 2004 and the SNP (Secondary Numeracy Project) followed in 2006. All of these projects have since terminated as most primary and intermediate schools have undergone the training and the 2011 was the final year for SNP schools. Another reason for termination was the National Party instigating National Standards in Numeracy and Literacy as an election promise. The funding for numeracy ceased and the funding for National Standards was created. The same people were involved in both projects. I was involved as a Mathematics Advisor implementing INP in 2005 and SNP in subsequent years through out the Waikato, BOP and Gisborne regions until 2010. [Update Nov 2011, funding for SSS has now ceased with contracts going to Cognition Auckland private provider for 2012 and 2013, afterwhich it will be given to schools. The funding has been reduced from previous levels for 2012].

The project created a huge resource of knowledge about how people learn mathematics. We learned that the thinking processes gain complexity and progress from being unable to count, to counting, to the more efficient adding, to the very efficient multiplying and thence to complex reasoning of proportional thinking. Problem solving was stressed at all times, explaining reasoning and proof likewise.

The data rich project established an EXPECTATION (see Appendix) chart based on data from schools that had undertaken a long-term numeracy development. The expectations are a little high but clearly show the transition of learning to


thinking mathematically. Around the same time the development of the “new” NZ Curriculum, implemented in 2010, began, again, largely by the same group of people. The net result is that the Mathematics and Statistics Curriculum is heavily embedded with numeracy principles, philosophy and learning.

The National Standards for Year 1 to 8 currently in vogue (see above) reflect much of the above but also high expectation of mathematics achievement for all students. Maori Achievement was identified as being slow and all projects including the Te Kotahitanga Project all aim to improve these levels. [Note the National Standards are “aspirational” in that they are quite high. Note also that dispite what the Year 8 standard says operating on rational numbers remains a CL5 task, not CL4 (whole numbers) as stated in the standard.]

During my time as advisor I was privileged enough to experience many conferences, conversations, workshops, presentations, overseas speakers and conferences and complete my own research to improve my understanding of learning to think mathematically. I implemented nearly $3M dollars of funding throughout Waikato and BOP schools in over 60 schools. I ran countless workshops and observed hundreds of teachers and students in action in their classrooms. I had the opportunity to discuss learning at length with many very clever teachers students of all abilities.

[What remains to be done is a NZ Numeracy Project Report giving regional and national views and summations of the project impact. This was singularly the largest investment, over $100M, in mathematics education ever undertaken in NZ. The questions of “What did we learn?” and “Was it worth it?” need to be considered. Thinking mathematically is important. Perhaps I will write a book.]

mathematics and statistics - reapschools.reap.org.nz/advisor/workshop 1/finished parts/s… ·...

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