The ProjecT · Web viewenable students to acquire confidence in developing strategies for dealing with new situations and problems provide opportunities for students to develop individual

International Baccalaureate DiplomaMathematical Studies 2017

The ProjecT

Information and Documentation Booklet

Progress sheet

Internal assessment details

Information: Skills and strategies required by students

Choosing a Project topic and descriptions of successful projects

Brainstorming sheet

Initial planning sheet

Information: How the project is assessed – Seven criteria and descriptors

Criterion A: Introduction

Criterion B: Information/measurement

Criterion C: Mathematical processes

Criterion D: Interpretation of results

Criterion E: Validity

Criterion F: Structure and communication

Criterion G: Commitment

Information: Approaches to project work

General hints for Maths Studies project

Spare paper for ideas/notes/graph drafts

Name: _________________________________________ Teacher: ________________

Year 12 IBDP

Maths Studies Project PROGRESS SHEET

Name:__________________________ Teacher: ________________

Term 1 Due Date Detail Comments Signatures

TransitionDecember

2016

Initial Planning/Brainstorm sheet

Week 210 February

Statement of TaskMake an appointment

with Mrs Graham to discuss task

Week 317 February

Collection/generation of Data

Week 53 March

Analysis/Interpretationof Data

Week 817 March

DRAFT DUE

Week 927-31 March

Discussion of draft. Make an appointment

with Mrs Graham

Term 2

Week 3May 1

PROJECT SUBMITTED,

4pm

Comments

Internal assessment details 20%

The purpose of the projectThe specific purposes of the project are to:

develop students' personal insight into the nature of mathematics and to develop their ability to ask their

own questions about mathematics

encourage students to initiate and sustain a piece of work in mathematics

enable students to acquire confidence in developing strategies for dealing with new situations and

problems

provide opportunities for students to develop individual skills and techniques and to allow students with

varying abilities, interests and experiences to achieve a sense of personal satisfaction in studying

mathematics

enable students to experience mathematics as an integrated organic discipline rather than fragmented and

compartmentalized skills and knowledge

enable students to see connections and applications of mathematics to other areas of interest

provide opportunities for students to show, with confidence, what they know and what they can do.

ObjectivesThe project is internally assessed by the teacher and externally moderated by the IBO. Assessment criteria have

been developed to address collectively all the group 5 objectives. In developing these criteria, particular attention

has been given to the objectives listed here, which are most satisfactorily assessed without the time constraints

imposed by written examinations.

Where appropriate in the project, students are expected to:

organize and present information and data in tabular, graphical and/or diagrammatic forms

know and use appropriate notation and terminology

recognize patterns and structures in a variety of situations, and make generalizations.

recognize and demonstrate an understanding of the practical applications of mathematics

use appropriate technological devices as mathematical tools

demonstrate an understanding of and the appropriate use of mathematical modelling.

RequirementsThe project is a piece of written work based on personal research involving the collection, analysis and

evaluation of data.

Each project must contain:

a title

a statement of the task

measurements, information or data which has been collected and/or generated

an analysis of the measurements, information or data

an evaluation of the analysis

a bibliography and footnotes, as appropriate.

Students can choose from a wide variety of project types, for example, modelling, investigations, applications

and statistical surveys. Historical projects that reiterate facts but have little mathematical content are not

appropriate and should be actively discouraged.

In developing their projects, students should make use of mathematics learned as part of the course. The level of

sophistication of the mathematics should be similar to that suggested by the syllabus. It is not expected that

students produce work that is outside the mathematical studies SL syllabus, and they are not penalized if they

produce such work.

LengthThe project should not normally exceed 2,000 words, excluding diagrams, graphs, appendices and bibliography.

However, it is the quality of the mathematics and the processes used and described that is important, rather than

the number of words written.

GuidanceWork set by the teacher is not appropriate for a project.All students should be familiar with the requirements of the project and the criteria by which it is assessed. In

particular, teachers should discuss with their students the levels of achievement expected for Criterion G,

Commitment. (More about this later)

It should be made clear to students that all work connected with the project, including the writing of the project,

should be their own.

Group work should not be used for projects. Each project should be based on different data collected or

measurements generated.

It must be emphasized that students are expected to consult the teacher throughout the process.

The teacher is expected to give appropriate guidance at all stages of the project by, for example, directing

students into more productive routes of inquiry, making suggestions for suitable sources of information, and

providing advice on the content and clarity of a project in the writing-up stage.

Teachers are encouraged to indicate to students the existence of errors but should not explicitly correct these

errors.

AuthenticityTeachers must ensure that each project is the student’s own work. If the teacher views the project at each stage of

its development, this serves as a very effective way of ensuring that the project is the intellectual property of the

student and also acts as a safeguard against plagiarism. In this way, by monitoring all stages of the development,

a teacher can ensure that the project is the authentic, personal work of the student.

All external sources quoted or used must be fully referenced by use of a full bibliography and footnotes.

If in doubt, authenticity may be checked by one or more of the following methods:

discussion with the student

asking the student to explain the methods used and to summarize the results/conclusions

asking the student to replicate part of the analysis using different data

asking the student to produce the sources used.

It is also appropriate for teachers to request that each project be signed on completion to indicate that it is the

student’s own work.

Skills and strategies required by students

PreparationChoosing a topic• Identifying an appropriate topic• Developing a topic into a more specific question• Devising a task that is well focused, well defined and appropriate• Expressing the task clearlyThese ideas are developed further in the section that gives details of how to choose a topic.Formulating a plan• Identifying clear boundaries for the task• Identifying the variables related to the task• Constructing a model of the plan for undertaking the task, or forming an outline of it.

Information/measurement• Identifying the type of data required• Identifying data that is relevant and appropriate to the task• Organizing ways of collecting data by, for example:

- carrying out surveys and questionnaires- counting- devising tests and/or measuring- conducting experiments- constructing diagrams, models, and so on- searching for data from reliable sources (for example, statistical records, the Internet)- using technology to generate data.

• Deciding how much data is appropriate• Being aware of sources of error and associated problems• Considering the reliability of various data-collection methods and of resource material• Organizing the data in a manner appropriate for further analysis

Mathematical processes• Selecting and using mathematical techniques relevant to the task

• Selecting and using technological devices as appropriate tools (for example, a graphic display calculator, computer software packages), making sure an understanding of the mathematical processes involved is demonstrated (this is developed further in the section on the use of technology)

• Making use of clearly labelled tables, graphs and diagrams to better illustrate mathematical processes

• Expressing results to an appropriate degree of accuracy

• Using SI (Système International) units of measurement

Interpretation and discussion of results• Interpreting the results obtained• Summarizing in words the information presented in a table, or represented in graphical or diagrammatic form• Comparing results obtained from different sets of data, or results obtained in different ways from the same set of data• Using the results obtained to generalize or make conjectures and from there to draw relevant conclusions• Commenting on sources of error within the project• Making relevant statements about the restrictive nature of the project• Identifying any assumptions that have been made• Discussing the validity of the processes used and of the results as a whole related skills and strategies

Validity• Discussing whether the mathematics used is appropriate• Discussing limitations of the processes used and conclusions drawn• Reflecting critically on the process as a whole

Structure and communication• Recording actions at each stage of the development of the project• Expressing ideas clearly• Using appropriate mathematical language and representation• Focusing on the task and not straying into other areas, and avoiding irrelevancies• Structuring ideas in a logical manner• Editing the text so that it flows• Proofreading the document for basic errors in spelling and grammarThese ideas are developed further in the section on integrating the project into the course of study.

Commitment• Initiating discussions with teachers or fellow students about project work• Contributing critically but positively to class discussions on project work• Organizing a series of goals and milestones within a personal time frame• Using teacher feedback to make improvements• Recognizing personal strengths and weaknesses• Appreciating the academic values associated with writing a project• Maintaining honesty and integrityThese ideas are developed further in the section on the supervision of students.

© International Baccalaureate Organization 2005

IntroductionThis section focuses on the importance of choosing a topic that can offer a productive route of inquiry, involve the use of relevant mathematics, and engage the interest and enthusiasm of the student.In particular, the first two parts of this section offer suggestions for suitable topics by:• listing the titles of successful projects that have been submitted in the past• providing descriptions of six successful projects.The third part suggests how students can find a suitable topic, and the fourth part gives ideas on how students can develop their initial ideas into suitable topics and how teachers can encourage students to become more focused through directed discussion.

Titles of successful projectsThe following list gives the titles of some successful projects submitted by students. Some titles are more descriptive than others and in most cases the original wording has been retained.

Aesthetics• Calculating beauty—the golden ratio• Colour preferences• Daylight in a classroom—architectural design• Illusions• Is my mirror showing an accurate image?• Origami applications to mathematics• Shadows and height

Business and finance• A comparative study of shares, real estate, bonds and banks• Analysis of stock market changes• Buying a car—payment options• Economic development and levels of income• Mortgage loans• Running a restaurant and dance club• Yen/dollar fluctuations

People• Aggression• Characteristics of federal prisoners• Gender based discrimination• Marriage celebrants• Perception of time• The psychology of memory• Voter turnout

Health and fitness• Breakfast and school grades• Breast and cervical cancer—ethnic comparison• Drug distribution• Infant mortality• Investigating reaction times• A comparison between lung capacity, age, weight and body fat

Titles of successful projects - ContinuedNature and natural resources• Analysis of the cost and utility of gas versus electricity in an average domestic situation• Calculating time of sunrise and sunset• Earthquakes• Kangaroo Island koalas• Stick nest rats• The quality of local water• Water, wine and roses

Food and drink• A comparison between calorie intake and gender• Dine in or dine out?• High school lunches• Jelly bean study• Take the cola challenge• The cookie problem—taste is all-important• The operation of a tuck shop

School-based titles• Alcohol consumption and teenagers• Girls’ sport and grades• Left-handed students• Performance of local students compared with foreign students• Searching for the ideal sound• Sport and nationality

Sport• Bat speed compared with body weight• Effective short corners in hockey• Factors affecting athletic performance• Height, weight and swimming performance• How far do tennis balls roll?• Resistance of fishing line• Stoppage times in National Football League (NFL) games• Will female swimmers ever overtake male swimmers?

Travel and transport• Air travel—distance compared with price• Cost efficiency of vehicles• Driving skills• Petrol prices• Seat belt use• Traffic movement in an urban area• Transport safety in town centres• Running late and driving habits

Miscellaneous• Astronomy• Average puppy weights in the first few weeks• Colour of words• Counting weeds• International phone call pricing• Memory• Practice makes perfect• Predicting cooling times• Shortest distance• Sine waves in pitch frequencies• Spanning trees• Topography and distance• Video games and response times• Volumes of partial spheres


Descriptions of successful projects

This section provides detailed descriptions of four successful projects that have been submitted by students in the past.

Driving skillsCollection of data

• Data was collected by means of a questionnaire. In total, 153 students completed a questionnaire asking for their gender, whether or not they had passed the driving theory examination and whether or not they had passed the driving practical examination.

Mathematical processes and interpretation of results

• A tally chart was used to collect the data, which was then set out neatly in tables. Percentages were calculated, pie charts were drawn and the chi-squared test was used to see if passing the theory examination was independent of gender and also if passing the practical examination was independent of gender.

• The student demonstrated a clear understanding of the mathematical processes involved and gave a clear justification for the use of these processes.

• The results showed that there was a difference between the result of the practical examination and the gender of the student, but that the result of the theory examination and gender of the student were independent.

Investigating reaction timesCollection of data

• Using a 30cm ruler, the student ensured that the thumb and index finger of each participant’s dominant hand were held five centimetres apart and that their arm was stretched out at a right angle. The ruler was held level with the top of the thumb and finger, and the instruction was given to each participant to catch the ruler when it was dropped. This process was repeated three times and the average reaction time was calculated for each participant. The same process was then repeated on each participant’s non-dominant hand.


• The data was set up in tables and displayed in bar graphs and scatter diagrams. The mean and standard deviation of the data for the dominant hand and non-dominant hand were calculated. Pearson’s product–moment correlation coefficient was calculated to find out if there was a connection between the reaction times of the dominant and non-dominant hands.


• Surprisingly, the results showed that the average reaction time for the non-dominant hand was slightly less than for the dominant hand. There was a weak, positive correlation between the reaction times of the two hands.


Descriptions of successful projects - Continued

Optimization of the volume of containersGeneration of measurements

• Measurements for several frustrum-shaped containers were generated using radii and heights. The surface areas and volumes of the frustrums were calculated; measurements of cylinders with the same volume as the frustrums and various ratios were also calculated.


• Similar figures were used to calculate the total height of the cones. Pythagoras’ theorem was used to calculate slant heights. The formulae for the volume and surface area of a cone were used to find the volume and surface area of the frustrums, and the formulae for the surface area and volume of a cylinder were used to find the dimensions of the cylinders. Clear diagrams were drawn and the information collected was set up in tables. Scatter diagrams were drawn and Spearman rank correlation coefficients were calculated.


• The results showed a very strong correlation between the ratio of the surface area/volume of the frustrums and the cylinders, but not between the ratio of the surface area/volume of the frustrums and the ratio of the radii.

Modelling periodic functions—investigating the motion of a bungee jumpGeneration of measurements

• Data was collected experimentally using a calculator-based ranger (CBR) and graphic display calculator (GDC). To model the motion of a bungee jump, a 200g weight and a 70cm length of elastic cord were used. The CBR was connected to the GDC and it recorded the motion of the function being modelled.

This information was then transmitted to the GDC in the form of a graph. The graph was used as the raw data for the experiment.


• Data was set up in tables and graphs were produced. A sinusoidal model that fitted the data needed

to be found. The equation used was . Various points on the curve were used to calculate the values of a, k, c and d. Because the maximum values were decreasing each time, the value for a was found using an exponential regression on the GDC.

• The final equation was entered into the GDC and graphed with the experimental data. The result was satisfactory. The curves were very similar, but not exactly the same.

The process of finding a suitable topicFor the majority of students, finding a suitable topic is the most difficult part of the project. Consequently, it is suggested that, as soon as students are ready to begin work on their projects, the teacher should allocate class time over two to three weeks to guide individual students through this

difficult process. Students should be expected to have one or two general ideas when they first meet the teacher.

At the start of the process, teachers should discuss with students the overall form of the assessment, as this may, in part, help to direct the flow of ideas and ultimately the focus of the project.

International Baccalaureate Organization 2005

Choosing a topic for your project

BRAINSTORMING: POSSIBLE PROJECT IDEAS

1. Complete the following chart about your hobbies or interests. This may be in sports, art, music, dance, the

environment, health, travel, trade, or commerce.

Hobby/Interest What maths might be involved?

Possible Project Direction

2. Here is a list of topics with which you should be familiar. Try to think of any "real world" situation that

might use some of these ideas. Try to link these topics with your hobbies listed above. Ask you teachers,

parents, and your friends to help you

Measurement Pythagorean Theorem

Area and Surface Area

Volume

Statistics

Linear Equations (Graphing)

Quadratic Equations (modelling)

Monetary Problems/Financial Mathematics

Probability

Ratio/Scale Drawing

Trigonometry/ SOHCAHTOA, sine rule, cosine rule

Perspective Drawing

Symmetry

Tessellations

Number Patterns

Sequences and Series

Forms for teachers and students

Mathematical Studies SL: The Project Form AInitial PlanningThis form should be completed and returned to your teacher by: Fri 6th Feb

Name:

1 Area of interest:

2 Topic:

3 Reason for choice

4 Statement of the task

5 Overall plan.

6 Method of data collection(For example, using: interviews, observations, questionnaires, constructing diagrams, playing games, experimenting. From: school, home, shops, journeys, newspapers, magazines, books, libraries, photographs, television, video, the Internet.)

7 Mathematical processes likely to be used in the analysis(For example, using: arithmetic sequences and series, geometric sequences and seriesinequalities, equations,sets, Venn diagrams, logic, truth tables sine rule, cosine rule, triangles, quadrilaterals, polygons, circles, cubes, cuboids, cylinders, prisms, spheres, geometric properties, trigonometric applications, vectors, scatter diagrams, lines of best fit, frequency tables, pie charts, bar charts, frequency histograms, frequency density histograms, cumulative frequency tables, cumulative frequency curves, percentiles, mean, median, mode, standard deviation, probability functions: linear, piece-wise, quadratic, trigonometric, exponential currency conversions, simple interest, compound interest, loan schemes, saving schemes, linear programming)

Forms for teachers and students

Approaches to project workInformation/measurements

The collection of data is fundamental to each project. It may be useful to discuss different aspects of data collection by trying to answer the questions listed below. Note: Raw data must be included with all projects.

What is data?Data can come in a number of forms, such as:

distances and angles, for an exercise on mapping

tide times and heights, which translate into coordinates for an exercise on trigonometric functions

shoe sizes and heights, for an exercise on correlation

diagrams of networks, for an exercise on transport routes between towns.

How much data is needed?The amount of data required depends on the task, as shown in the following examples.

An exercise on mapping an area of land would require sufficient bearings and distances to locate all the vertices of the region.

The quantity of data needed for an activity based on tides, their times and heights would depend on the parameters of the exercise. If the aim were to look at daily variations in height then measurements would need to be taken hourly over the specified period of time. If the exercise were concerned with seasonal variations then it could be that measurements need only be taken daily.

The data needed for an exercise on the correlation between shoe size and height should draw from as wide a group as possible, taking into account factors such as age.

The number of roads represented in a network for an exercise based on traffic flow would depend on the specific nature of the task. For example, if the exercise is concerned with the movement of heavy vehicles then all the roads that are used by these vehicles should appear in the network.

Students must know that all expected values for a chi-squared test must be greater than 5.

Where can data be collected?Students need to be made aware of the sources of data available. For example, students can:

take measurements using a whole range of measuring instruments, such as rulers, tape measures, compasses, protractors, scales and electronic devices

collect data through surveys and questionnaires

obtain information from published tables, such as timetables and loan-repayment schedules

search the Internet

refer to sources that publish statistical data

take photographs

generate data by investigating different situations, such as the construction of geometrical shapes

carry out experiments.

Designing a questionnaireThere is skill involved in structuring a questionnaire to elicit the required information. The guidelines suggested below can assist students in writing questionnaires.The questions should be:

clearly and courteously phrased

few in number

capable of being answered by any person questioned

capable of being answered easily and in a defined manner, for example, yes or no, a number, a place, a

name

capable of being answered truthfully and willingly

regarded as being non-intrusive by those questioned.

The author of the questionnaire should always be identified and the reason for seeking the requested information should be explained. It is always advisable to trial the questionnaire on a small group first so that the questions can be refined before it is distributed to a wider audience.

Mathematical processesIt is important for students to understand that they should only employ techniques that are relevant to the stated task. Consequently, students should ask certain questions, such as the following.

Is it appropriate to use this technique?

What information will it provide?

Is there an alternative technique?

Which is the best technique to use?

By asking these questions within the context of the project and writing down reasons for their choice of technique, students will be able to demonstrate their understanding of the concepts concerned. This becomes particularly important when students use computer software packages or GDCs.

Note: using a number of different types of graphs to represent the same data and obtain the same information does not constitute a wide range of mathematical techniques.

Interpretation of resultsThroughout the course, students should reflect on the significance of their results and to consider what conclusions can be drawn. Emphasis should also be placed on whether a set of results and the conclusions drawn from it are consistent with the analysis.

ValidityStudents need to give particular attention to the concept of validity

The following questions need to be considered by students.

Are the processes used appropriate and relevant to the project?

What are the limitations of the particular processes used in the context of the project?

What refinements might have been considered?

Validity - ContinuedSuggestions for refinement might include the obvious one of obtaining more data. However, this increase in data alone, without further discussion, will not always be sufficient to increase a student’s mark in criterion E.

Further examples of such refinement might include a discussion of alternative statistical tests, speculation about alternative functions to model data, mention of alternative regression techniques, or perhaps piecewise regression. For example, perhaps data that looks linear over a large range of values might look more quadratic from further away. Perhaps a sinusoidal-looking function has a slowly varying amplitude that has not been accounted for by the suggested model. Speculation about a damping function or a modulating function is likely to lead to higher marks. Such refinements need not be actually implemented, but awareness of the possibilities can improve the marks awarded for criterion E.

Structure and communicationStructuring the writing up of a project is a skill that needs to be recognized.

It may also help to consider certain sections as questions. For example:

Statement of the task: what is the aim of the investigation?

Plan: how is the investigation going to be approached?

Conclusion: what do the data and analysis say about the original task?

Students should use appropriate mathematical notation and terminology at all times.

References and bibliographyStudents should be aware that direct or indirect use of the words of another person, (in written, oral or electronic formats), must be acknowledged appropriately, as must any visual material used in the project that has been derived from another source. A student’s failure to comply with this requirement will be viewed as plagiarism, and, as such, may be treated as a case of malpractice.

The bibliography or list of references should include only those works (for example, books and journals) that the student has consulted while working on the project. An accepted form of quoting and documenting sources should be applied consistently. The major documentation systems are divided into two groups: parenthetical in-text systems and numbered systems. Either may be used, provided this is done consistently and clearly.

Each work consulted, regardless of whether or not it has already been cited as a reference, must be listed in the bibliography. The bibliography should specify: author/s, title, date and place of publication, and the name of the publisher, and should follow consistently one standard method of listing sources. Possible examples are:

Peterson, A D C. Schools Across Frontiers: the story of the International Baccalaureate and the United World Colleges. La Salle, Illinois: Open Court, 1987.

Institute for Aerospace Research (IAR). Flight Research. In National Research Council of Canada (NRC) [online]. 1996 [cited 1996-07-11]. Available from World Wide Web: <URL: http://www.iar.nrc.ca/iar/fr_general-e.html>

Zieger, Herman E. “Aldehyde”. The Software Toolworks Multimedia Encyclopedia. Vers. 1.5. Software Toolworks. Boston: Grolier, 1992.

Bruckman, Amy S. “MOOSE Crossing Proposal”. [email protected] (20 Dec. 1994).

Note that for personal e-mail listings the address should be omitted.

http://www.iar.nrc.ca/iar/fr_general-e.html

Internal assessment criteriaThe project is internally assessed by the teacher and externally moderated by the IBO using assessment criteria that relate to the objectives for group 5 mathematics.

Form of the assessment criteriaEach project should be assessed against the following seven criteria:

Criterion A Introduction

Criterion B Information/measurement

Criterion C Mathematical processes

Criterion D Interpretation of results

Criterion E Validity

Criterion F Structure and communication

Criterion G Commitment.

Applying the assessment criteriaThe method of assessment used is criterion referenced, not norm referenced. That is, the method of assessing each project judges students by their performance in relation to identified assessment criteria and not in relation to the work of other students.

Each project submitted for mathematical studies SL is assessed against the seven criteria A to G. For each assessment criterion, different levels of achievement are described that concentrate on positive achievement. The description of each achievement level represents the minimum requirement for that level to be achieved.

The aim is to find, for each criterion, the level descriptor that conveys most adequately the achievement levels attained by the student.

Read the description of each achievement level, starting with level 0, until one is reached that describes a level of achievement that has not been reached. The level of achievement gained by the student is therefore the preceding one and it is this that should be recorded.

For example, if, when considering successive achievement levels for a particular criterion, the description for level 3 does not apply then level 2 should be recorded.

For each criterion, whole numbers only may be recorded; fractions and decimals are not acceptable.

The highest achievement levels do not imply faultless performance and teachers should not hesitate to use the extremes, including zero, if they are appropriate descriptions of the work to be assessed.

The whole range of achievement levels should be awarded as appropriate. For a particular piece of work, a student who attains a high achievement level in relation to one criterion may not necessarily attain high achievement levels in relation to other criteria.

A student who attains a particular level of achievement in relation to one criterion does not necessarily attain similar levels of achievement in relation to the others. Teachers should not assume that the overall assessment of the students produces any particular distribution of scores.

It is recommended that the assessment criteria be available to students at all times.

The final markThe final mark for each project is the sum of the scores for each criterion.

The maximum possible final mark is 20.

Achievement levelsCriterion A: IntroductionIn this context, the word “task” is defined as “what the student is going to do”; the word “plan” is defined as “how the student is going to do it”. A statement of the task should appear at the beginning of each project. It is expected that each project has a clear title.

Achievement Level Descriptor

0 The student does not produce a clear statement of the task.

There is no evidence in the project of any statement of what the student is going to do or has done.

1 The student produces a clear statement of the task.

For this level to be achieved the task should be stated explicitly.

2 The student produces a title, a clear statement of the task and a clear description of the plan.

The plan need not be highly detailed, but must describe how the task will be performed.

Criterion B: Information/MeasurementIn this context, generated measurements include those that have been generated by computer, by observation, by investigation, by prediction from a mathematical model or by experiment.Mathematical information includes geometrical figures and data that is collected empirically or assembled from outside sources. This list is not exclusive and mathematical information does not solely imply data for statistical analysis.


0 The student does not collect relevant information or generate relevant measurements.

No attempt has been made to collect any relevant information or generate any relevant measurements.

1 The student collects relevant information or generates relevant measurements.

This achievement level can be awarded even if a fundamental flaw exists in the instrument used to collect the information, for example, a faulty questionnaire or an interview conducted in an invalid way.

2 The relevant information collected, or set of measurements generated by the student, is organized in a form appropriate for analysis or is sufficient in both quality and quantity.

A satisfactory attempt has been made to structure the information/measurements ready for the process of analysis, or the information/measurements are adequate in both quantity and quality.

3 The relevant information collected, or set of measurements generated by the student, is organized in a form appropriate for analysis and is sufficient in both quality and quantity.

This level cannot be achieved if the measurements/information are too sparse (that is, insufficient in quantity) or too simple (for example, one-dimensional) as clearly it does not lend itself to being structured. It should therefore be recognized that within this descriptor there are assumptions about the quantity and, more importantly, the quality (in terms of depth and breadth) of information or measurements generated.

Criterion C: Mathematical processesWhen presenting diagrams, students are expected to use rulers where necessary and not merely sketch.A freehand sketch would not be considered a correct mathematical process. When technology is used the student would be expected to show a clear understanding of the mathematical processes used.


0 The student does not attempt to carry out any mathematical processes.

This would include students who have copied processes from a book with no attempt being made to use their own collected/generated information.

Projects consisting of only historical accounts, for example, will achieve this level.

1 The student carries out simple mathematical processes.

Simple processes are considered to be those that the average mathematical studies student could carry out easily, for example, percentages, areas of plane shapes, linear and quadratic functions (graphing and analysing), bar charts, pie charts, mean and standard deviation, simple probability. This level does not require the representation to be comprehensive, nor does it demand the calculations to be without error.

2 The simple mathematical processes are mostly or completely correct, or the student makes an attempt to use at least one sophisticated process.

Examples of sophisticated processes are volumes of pyramids and cones, analysis of trigonometric and exponential functions, optimization, statistical tests and compound probability. For this level to be achieved it is not required that the calculations for the sophisticated process(es) be without error.

3 The student carries out at least one sophisticated process, and all the processes used are mostly or completely accurate.

The key word in this descriptor is “accurate”. It is accepted that not all calculations need to be checked before awarding this achievement level; random checking of some calculations is sufficient. A small number of isolated mistakes should not disqualify a student from achieving this level. However, incorrect use of formulae, or consistent mistakes in using data, would disqualify the student from achieving this level.

4 The student carries out at least one sophisticated process; the processes used are mostly or completely accurate and all the processes used are relevant.

For this level to be achieved the mathematical processes must be appropriate and used in a meaningful way.

5 The student accurately carries out a number of relevant sophisticated processes.

To achieve this level the student would be expected to have carried out a range of meaningful mathematical processes. The processes may all relate to a single area of mathematics, for example, geometry. Measurements, information or data that are limited in scope would not allow the student to achieve this level.

Criterion D: Interpretation of resultsUse of the terms “interpretations” and “conclusions” refers very specifically to statements about whatthe mathematics used tells us after it has been used to process the original information or data. Wider discussion of limitations and validity of the processes is assessed elsewhere.


0 The student does not produce any interpretations or conclusions.

For the student to be awarded this level there must be no evidence of interpretation or conclusions anywhere in the project, or a completely false interpretation is given without reference to any of the results obtained.

1 The student produces at least one interpretation or conclusion.

Only minimal evidence of interpretations or conclusions is required for this level. This level can be achieved by recognizing the need to interpret the results and attempting to do so, but reaching only false conclusions.

2 The student produces at least one interpretation and/or conclusion that is consistent with the mathematical processes used.

For this level to be achieved at least one interpretation and/or conclusion is required. A “follow through” procedure should be used and, consequently, it is irrelevant here whether the processes are either correct or appropriate; the only requirement is consistency.

3 The student produces a comprehensive discussion of interpretations and conclusions that are consistent with the mathematical processes used.

To achieve this level the student would be expected to produce a meaningful discussion of the results obtained and the conclusions drawn. In this context, the word “comprehensive” should be taken to mean thorough and detailed discussion of interpretations based on the level of understanding reasonably to be expected from a student for mathematical studies SL. This achievement level cannot be awarded if the project is a very simple one, with few opportunities for substantial interpretation. This level would not be achieved with too many incorrect interpretations or conclusions present.

Criterion E: Validity

An important distinction is drawn between interpretations and conclusions, and validity. Validity addresses the questions as to whether appropriate mathematics was used to deal with the information collected and whether the mathematics used has any limitations in its applicability within the project.Any limitations or qualifications of the conclusions and interpretations should also be judged within this criterion. The considerations here are independent of whether the particular interpretations and conclusions reached are correct or adequate.


0 The student does not comment on the mathematical processes used or the interpretations/ conclusions made.

There is no attempt to evaluate (as opposed to interpret) the project to assess the validity of the mathematical processes or model used.

1 The student has made an attempt to comment on either the mathematical processes used or the interpretations/conclusions made.

The student shows an awareness of the possibility that some or all of the results may have a limited validity and makes an attempt to discuss the reasons for such limitations. Statements merely acknowledging the need for more information/measurements, but with no further evaluation, belong in this achievement level. If it is believed that validity is not an issue, this must be stated with at least some reasonable justification for the belief.

2 The student has made a serious attempt to comment on both the mathematical processes used and the interpretations/conclusions made.

There is significant discussion of the validity of the techniques used, recognition of any limitations that might apply and at least one realistic suggestion for improvement. A statement such as “I should have used more information/measurements” without further clarification, is not sufficient to earn full marks for this criterion. If the student considers that validity is not an issue, this must be fully justified, and can only achieve this achievement level if the argument is reasonable.

If the discussion of validity is clearly worth achievement level 1 and is then supplemented with sensible suggestions for extension of the project, this can also assist in the achievement of this level though such suggestions alone are not adequate if there is no discussion of validity.

Criterion F: Structure and communicationThe term “structure” should be taken primarily as referring to the organization of the information, calculations and interpretations in such a way as to present the project as a logical sequence of thought and activities starting with the task and the plan, and finishing with the conclusions and limitations. The term “communication” refers primarily to the correct and effective use of mathematical notation and sensible choice of diagrammatic and tabular representations. It is not expected that spelling, grammar and syntax are perfect and these features are not judged in assigning a level for this criterion. Nevertheless, teachers are strongly encouraged to correct and assist students with the linguistic aspects of their work. Projects that are very poor linguistically are also less likely to excel in the areas that are important in this criterion.


0 The student has made no attempt to structure the project.

It is not expected that many students will be awarded this level.

1 The student has made some attempt to structure the project or has used appropriate notation and terminology.

There must be a logical development to the project or the appropriate notation and terminology must be used correctly.

2 The student has made some attempt to structure the project and has used appropriate notation and terminology.

There must be a logical development to the project and the appropriate notation and terminology must be used correctly

3 The student has produced a project that is well structured and communicated in a coherent manner.

To achieve this level the project would be expected to read well, and contain footnotes and a bibliography, as appropriate.

Criterion G: CommitmentThe project should be an ongoing process involving consultation between student and teacher. The student should be aware of the expectations of the teacher from the beginning of the process and each achievement level awarded should be justified by a written comment from the teacher at the time of marking. The examples given below for each criterion level are teacher orientated and each teacher should use discretion when judging the levels.


0 The student showed little or no commitment.For example, the student did not participate in class discussions on project work, did not submit the required work in progress, and/or missed many deadlines.

1 The student showed satisfactory commitment.For example, the student participated in class discussions on project work, kept to most deadlines, had some discussion initiated by the teacher but did not necessarily exploit all the available opportunities for the development or improvement of the project.

2 The student showed full commitment.For example, the student participated fully in class discussions on project work, took initiatives both in discussion with the teacher and/or the rest of the class and in subsequent work of a more independent nature and/or demonstrated a full understanding of all the steps in the development of his/her project.To obtain the highest achievement level for this criterion the student should have excelled in several areas such as those listed below. This list is not exhaustive and teachers are encouraged to add their own expectations.The student:

actively participated at all stages of the development of the project

demonstrated a full understanding of the concepts associated with his/her project

participated in class activities on project work demonstrated initiative demonstrated perseverance showed insight prepared well to meet deadlines set by the teacher.

General hints for Maths Studies project Read criteria carefully!!

Structure/Communication - units, labels/scales on graphs, multiple graphs on one set of axes – use colour and label carefully, domain on all graphs – also be careful of showing relevant areas of the axes. Do graphs on computer as much as possible. Decimal places/sig figs consistent and relevant to your project. Does it flow (get someone who hasn’t read your project to read it for you and comment critically on it), point form OK , general presentation – handwritten OK, use colour, boxes, bold, easy to read font. Mathematical formula using equation editor – do not use 3^4 or 2/5 etc. Spreadsheet formula OK but then also write mathematical formula and explain. Define all terms/ variables. Sometimes it is best to do the maths by hand, “=” underneath one another. Units! Use careful headings and subheading.. Spread calculations out – leave a line between each stage.

Make sure that your statement of task is well focused – ie does your project do what your statement task says it will do?

Can the reader read the statement of task, each of the headings and subheadings and the conclusions and get a good feel for the whole of your project?

Page numbers on each page. Refer carefully to appendices (App 2, page 206)

Make sure you explain every step - even if it seems obvious to you, and try to relate it back to your aims. This is important for Criterion A and E. Use simple language.

Introduction/statement of task – include aim/hypothesis and maths to be used (see method below) and concise plan.

Method – include mathematics to be used, introduction/overview at start and then can be spread out through the project/interspersed with results and comments – often enhances flow and communication of the project

Results - TRIPLE CHECK ALL MATHS CALCULATIONS (Crit C). Define all variables

Evaluations – can be done as you go along, remember to comment on how valid your results are (Crit D) include ideas for further investigation. Interpret, interpret, and interpret!

Conclusion – have you answered the aim/hypothesis? Include validity discussion and further investigations.

Acknowledgements – of person who has helped you and what they have helped you with

Appendices - for repetitive stuff

Bibliography - if needed – for websites as well as books

No names – candidate number on each sheet and on front cover sheet. Nothing fancy needed. No Wesley College or Mrs Graham.

Word count roughly 2000 – but don’t stress too much about this. Spelling check!

Hand in, in plastic sleeve, stapled in top left hand corner. Hand in original, photocopy and electronic copy, please.

DUE 01 MAY 2017 ABSOLUTELY NO EXTENSIONS

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