- Geometry and Spatial Sense -

Overview of Website Organization:

1.  Task Summary - Teacher's Manual of Chess Lessons

2.  Website Navigational Aids - Teacher/Student Hubs

3.  Ontario Ministry of Education Mathematics Expectations for Grade 4 and Achievement Chart

4.  Task Content - Chess Lesson Plans Integrated with Current Ontario Mathematics Curriculum

5.  Teaching/Learning Strategies and Adaptations

6.  Prior Knowledge - Mathematics/Chess/Internet

7.  Unit Resources - Ministry Guidelines/Computer Programs

8.  Additional Resources - Internet Links/References/Rubric Resources

9.  Culminating Task - Chess Tournament

10. Assessment - Growth Scheme for Chess/Achievement Chart

Raison d'etre

The beauty of chess is that it allows the spontaneous flow of many skills to emerge simultaneously, stimulating a child's mind in a mentally challenging environment.  By appealing to a student's mental faculties, the student can proactively and independently excel at their own rate and can track his/her own progress throughout their development.

Chess instruction is not intended be a stand alone subject, rather in the format to be developed, the primary purpose is to serve as an additional instrument - a vehicle for instruction and experiential learning (as well as any additional benefit that may also be enjoyed).  Developing chess skill at an early age will undoubtedly inspire future chess proficiency and increase skill and acumen in other areas as well.  Chess is the aerobics of the mind.  Chess has been shown to improve academic performance.  Children taking part in a chess program develop critical thinking, logic, reasoning, and problem solving abilities, memory, concentration and visualization skills, confidence, patience, determination, poise, self-expression, and good sportsmanship.  Perhaps more importantly, children who participate in chess programs improve their self-esteem.

The instructional unit will address the following questions:

- What will the students learn?

- What evidence would prove that learning has occurred?

- How can one design performance tasks to provide evidence of learning?

- What criteria will be used to assess and evaluate learning?

- What assessment strategies will be utilized to aid in assessment and evaluation?

Instruction through game playing is one of the most effective motivational tools in a teacher's repertoire.  Children love games.  Chess is a game which motivates students in logical problem solving through developing their geometrical abilities and spatial understanding.  Students will spend hours quietly immersed in logical thinking where often these same students may not sit still through traditional methods of instruction in a regular classroom setting.

Chess education is extremely effective with children because chess:

- develops concentration;
- requires foresight and cultivates visualization skills;
-  builds technological (computer) skills;
- involves all levels of critical thinking (knowledge, comprehension, analysis, evaluation, predicting outcomes);
- improves memory skills;
- teaches how to think logically and efficiently, learning to select the 'best' choice from a large number of options;
- improves problem solving skills;
- raises self-esteem by encouraging children to overcome the fear of risk-taking;
- teaches self-discipline;
- develops an appreciation for the talents of others;
- values the spirit of true sportsmanship;
- enables children to assume responsibility for their decisions;
- raises intelligence quotient (IQ) scores;
- teaching how to make difficult and abstract decisions independently;
- enhances reading, memory, language, and mathematical abilities;
- fosters critical, creative, and original thinking;
- provides practice at making accurate and fast decisions under time pressure, a skill that can help improve exam scores at school;
- challenges self-motivated gifted children, while potentially helping underachieving students learn how to study and strive for excellence;
- demonstrate the importance of flexible planning, concentration, and the consequences of decisions;    
 - reaches both boys and girls regardless of their natural abilities or socio-economic backgrounds;
- rewards determination and perseverance;
- facilitates lasting and long range friendships;
- encourages socialization skills that extend across cultures and generations for a lifetime of learning enjoyment;
- shows quiet activities can be fun, and most of all chess is fun!  

Lesson Plans:

Ontario Ministry of Education Mathematics Curriculum for Grade 4 is integrated and organized into chess lessons.  These lessons start with basic concepts and gradually progress through a series of steps that introduce the student to more complex topics, including how pieces move, capture and the coordination of pieces to checkmate an opponent.

Sequentially delivered (meta-method) chess lessons developed for enhancing students' Mathematical ability in Geometry and Spatial Sense include:

Lesson 1 - The chessboard and names of pieces

Lesson 2 - Starting the game

Lesson 3 - How pawns move and capture

Lesson 4 - How rooks move and capture

Lesson 5 - How bishops move and capture

Lesson 6 - How knights move and capture

Lesson 7 - How queens move and capture

Lesson 8 - How kings move and capture

Lesson 9 - When a pawn becomes a queen

Lesson 10 - Castling

Lesson 11 - Check!

Lesson 12 - Checkmate!

Lesson 13 - Counting points

Lesson 14 - Win, lose or draw

Culminating Activity:  Chess tournament

Computer Chess Lesson(s) - Meta-method Approach:

The student will learn how to play the game of chess using the meta-method of teaching strategies:

 - providing opportunities for manipulation and experimentation without rule identification.

- demonstration without rule identification/conceptual development.

- modelling with rule identification as a performance task.

- interactive play, peers/pairs and computer guided problem solving.

- self-directed study developing both procedural knowledge and    strategy.

- assessment by teacher using a Growth Scheme.

Instructional Aids:

A list of unit wide resources include: demonstration board, class chess sets, computers and computer graphics - chess pieces and chess board graphics, links to other instructional chess websites. Note: copyright and/or permission has been expressly granted for educational use only (see Disclaimer).

Recommended are standard 'Staunton' design, solid plastic chess pieces, on a laminated paper board with alphanumeric borders and 2" squares.  These can be purchased from the Chess Federation of Canada at educational discounted prices from the C.F.C. official website: www.chess.ca.

Students will be required to be computer literate and able to read and follow electronic cues for instructions, following examples as presented in the sequentially delivered (meta-method) chess lessons developed for the ChessMateOntario.com website.

The Student Resource page of the ChessMateOntario website is self-guiding, however introduction and personal mentoring is strongly recommended.  As students work through the lessons, problems will be presented to them. A teacher or tutor may be required to encourage or assist students through the lesson or situational problem, as specific difficulties may be encountered. Observation of student progress and formative assessment is an ongoing process.

Also, if a classroom has for example twenty students, ten chess boards will be required. Chess supplies may be purchased via the Chess Federation of Canada website (www.chess.ca).  A large demonstration board would be an asset.  This will enable the entire class to view without having to crowd around a small tabletop set.  Student access to computers would be required.  Students may be paired or work independently on the ChessMateOntario website (certified "kid-friendly").

Evaluation and Assessment:

Anecdotal Record - Use anecdotal record noting student performance and behaviour.

Checklist - Teacher to observe and check students' performance.

Rating Scale - Growth Scheme

Rubric - Achievement Chart 

Select Response - chess quiz

Summative and formative evaluation tools:

Achievement Chart - The Achievement Chart as outlined by the Ontario Ministry of Education guidelines for Mathematics Grade 4: Geometry and Spatial Sense.  The ChessMateOntario website has adapted student achievement following a program of chess instruction.

Expectations -  Both General and Specific Expectations as found in the Ontario Achievement Chart for Mathematics - Grade 4: Geometry and Spatial Sense, including additional expectations (see below).

Growth Scheme - An assessment tool for measuring chess skill and aptitude using the meta-method approach.  This tool may be used as an additional measuring device or as a checklist for assessing student growth and development in chess (see: Teacher Tools).

Self Assessment - independent learning provided by guided exploration on ChessMateOntario.com website.

Early Math Strategies - for Geometry and Spatial Sense, developed by the Ontario Ministry of Education using:

a) Achievement Chart - (Ontario curriculum policy document)

b) Achievement Levels (provincial standards)

c) Assessment & Evaluation - teacher/peer/self

d) Conceptual Development

e) Conceptual Understanding

f) Developmental Stages (intellectual/emotional/social moral)

g) Expectations (four different degrees of provincial expectations)

h) Instructional Leader/Conferencing/Mentor(teacher/tutor/peer/computer)

i) Intervention/Prompt

j) Learning Styles (visual/auditory/tactile & kinaesthetic exploratory)

k) Mathematical Concepts (Strand: Geometry and Special sense)

l) Manipulatives (concrete materials such as chess pieces)

m) Model (manipulative)

n) Modelling (demonstration)

o) Multiple Intelligences

p) Representation

q) Performance Task

r) Problem Solving

s) Procedural Knowledge/Scaffolding

t) Remediation (Provision of special instructional assistance to students experiencing difficulty)

In addition:

Addendum:

According to the Overall Expectations for students based on the Ontario Ministry of Education Curriculum Guidelines, it will be assumed by the end of Grade 3, students will have:

- investigated the attributes of three-dimensional figures and two-dimensional shapes using concrete materials and drawings;

- drawn and built three-dimensional objects and models;

- explored transformations of geometric figures;

- understood key concepts in transformational geometry using concrete materials and drawings;

- described location and movements on a grid;

- used language effectively to describe geometric concepts, reasoning, and investigations.

Six of the Ontario Ministry of Education expectations for Mathematics: Geometry and Spatial Sense (Grade 4) are not addressed in this chess unit. These expectations may be taught using a more traditional approach to Geometry.

These exceptions are:

Two and three dimensional Geometry:

4m64 - explore transformations of geometric figures;

4m69 - sketch the faces that make up a three-dimensional figure using concret materials as models;

4m71 - identify and sort quadrilaterals (e.g., square, trapezoid);

4m76 - measure angles using a protractor;

4m78 - recognize and describe the occurrence and application of geometric properties and principles in the everyday world;

4m84 - draw lines of symmetry on two-dimensional shapes.

However, eight additional Ontario Ministry of Education expectations for Mathematics (Grade 4), can be applied to chess instruction following this program.

These additional expectations are:

Patterning and Algebra:

4m86 - demonstrate an understanding of mathematical relationships in patterns using concrete materials, drawings, and symbols;

4m87 - identify, extend, and create linear and non-linear geometric patterns, number and measurement patterns, and patterns in their environment;

4m88 - recognize and discuss patterning rules;

4m89 - apply patterning strategies to problem-solving situations:

4m95 – use a calculator and computer applications to explore patterns;

4m96 – pose and solve problems by applying a patterning strategy (e.g., solve an area problem by extending a geometric grid pattern);

4m98 – discuss and defend the choice of a pattern rule;

4m99 – given a rule expressed in informal language, extend a pattern.

Source: [online]

http://www.edu.gov.on.ca/eng/document/curricul/curr97ma/geometry.html

Note:  A further correlation between Geometry and Spatial Sense to Patterning and Algebra exists in chess instruction.  For example, when using the alpha-numeric chess notation of a chess board as an algebraic expressing of location or movement on a grid (i.e. as an opening move, C2 - C4).