Interactive Maths - The Interactive Way to Teach Mathematics
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  • Number
    • Arithmetic >
      • The Four Operations >
        • The Four Operations (QQI)
        • The Four Operations (10QQI)
        • The Four Operations (QQI Count Down)
        • The Four Operations (QQI Relay)
        • The Four Operations (QQI BINGO)
        • The Four Operations (QQI Worksheets)
        • The Four Operations (Video)
        • Timestables Square (QQI)
        • Grid Multiplication (QQI)
      • Missing Numbers >
        • Missing Numbers (QQI)
        • Missing Numbers (10QQI)
        • Missing Numbers (QQI Count Down)
        • Missing Numbers (QQI Relay)
        • Missing Numbers (QQI BINGO)
        • Missing Numbers (QQI Worksheets)
      • Order of Operations >
        • Order of Operations (QQI)
        • Order of Operations (10QQI)
        • Order of Operations (QQI Count Down)
        • Order of Operations (QQI Relay)
        • Order of Operations (QQI BINGO)
        • Order of Operations (QQI Worksheets)
      • Powers of Ten >
        • Powers of Ten (QQI)
        • Powers of Ten (10QQI)
        • Powers of Ten (QQI Count Down)
        • Powers of Ten (QQI Relay)
        • Powers of Ten (QQI BINGO)
        • Powers of Ten (QQI Worksheets)
      • Decimal Operations >
        • Decimal Operations (QQI)
        • Decimal Operations (10QQI)
        • Decimal Operations (QQI Count Down)
        • Decimal Operations (QQI Relay)
        • Decimal Operations (QQI BINGO)
        • Decimal Operations (QQI Worksheets)
      • Rounding >
        • Rounding (QQI)
        • Rounding (10QQI)
        • Rounding (QQI Count Down)
        • Rounding (QQI Relay)
        • Rounding (QQI BINGO)
        • Rounding (QQI Worksheets)
      • Products and Sums (QQI)
      • Products and Sums (10QQI)
    • Fractions >
      • Cancelling Fractions >
        • Cancelling Fractions (QQI)
        • Cancelling Fractions (10QQI)
        • Cancelling Fractions (QQI Count Down)
        • Cancelling Fractions (QQI Relay)
        • Cancelling Fractions (QQI BINGO)
        • Cancelling Fractions (QQI Worksheets)
      • Mixed Numbers and Improper Fractions >
        • Mixed Numbers and Improper Fractions (QQI)
        • Mixed Numbers and Improper Fractions (10QQI)
        • Mixed Numbers and Improper Fractions (QQI Count Down)
        • Mixed Numbers and Improper Fractions (QQI Relay)
        • Mixed Numbers and Improper Fractions (QQI BINGO)
        • Mixed Numbers and Improper Fractions (QQI Worksheets)
      • Fractions of Amounts >
        • Fractions of Amounts (QQI)
        • Fractions of Amounts (10QQI)
        • Fractions of Amounts (QQI Count Down)
        • Fractions of Amounts (QQI Relay)
        • Fractions of Amounts (QQI BINGO)
        • Fractions of Amounts (QQI Worksheets)
      • Fraction Arithmetic >
        • Fraction Arithmetic (QQI)
        • Fraction Arithmetic (10QQI)
        • Fraction Arithmetic (QQI Count Down)
        • Fraction Arithmetic (QQI Relay)
        • Fraction Arithmetic (QQI BINGO)
        • Fraction Arithmetic (QQI Worksheets)
    • FDP >
      • Fraction Decimal Conversions Drill
    • Percentages >
      • Percentages of Amounts >
        • Percentages of Amounts (QQI)
        • Percentages of Amounts (10QQI)
        • Percentages of Amounts (QQI Count Down)
        • Percentages of Amounts (QQI Relay)
        • Percentages of Amounts (QQI BINGO)
        • Percentages of Amounts (QQI Worksheets)
        • Percentage of Amounts (Video)
      • Writing Numbers as a Percentage >
        • Writing Numbers as a Percentage (QQI)
        • Writing Numbers as a Percentage (10QQI)
        • Writing Numbers as a Percentage (QQI Count Down)
        • Writing Numbers as a Percentage (QQI Relay)
        • Writing Numbers as a Percentage (QQI BINGO)
        • Writing Numbers as a Percentage (QQI Worksheets)
        • Writing Numbers as a Percentage (Video)
      • Percentage Change >
        • Percentage Change (QQI)
        • Percentage Change (10QQI)
        • Percentage Change (QQI Count Down)
        • Percentage Change (QQI Relay)
        • Percentage Change (QQI Worksheets)
        • Percentage Change (Video)
      • Increase and Decrease by a Percentage >
        • Increase and Decrease by a Percentage (QQI)
        • Increase and Decrease by a Percentage (10QQI)
        • Increase and Decrease by a Percentage (QQI Count Down)
        • Increase and Decrease by a Percentage (QQI Relay)
        • Increase and Decrease by a Percentage (QQI BINGO)
        • Increase and Decrease by a Percentage (QQI Worksheets)
        • Increase and Decrease by a Percentage (Video)
      • Compound Interest and Simple Interest >
        • Compound Interest and Simple Interest (QQI)
        • Compound Interest and Simple Interest (10QQI)
        • Compound Interest and Simple Interest (QQI Count Down)
        • Compound Interest and Simple Interest (QQI Relay)
        • Compound Interest and Simple Interest (QQI BINGO)
        • Compound Interest and Simple Interest (QQI Worksheets)
        • Compound Interest and Simple Interest (Video)
      • Overall Percentage Change >
        • Overall Percentage Change (QQI)
        • Overall Percentage Change (10QQI)
        • Overall Percentage Change (QQI Count Down)
        • Overall Percentage Change (QQI Relay)
        • Overall Percentage Change (QQI BINGO)
        • Overall Percentage Change (QQI Worksheets)
      • Reverse Percentages >
        • Reverse Percentages (QQI)
        • Reverse Percentages (10QQI)
        • Reverse Percentages (QQI Count Down)
        • Reverse Percentages (QQI Relay)
        • Reverse Percentages (QQI BINGO)
        • Reverse Percentages (QQI Worksheets)
        • Reverse Percentages (Video)
      • Mixed Percentages >
        • Mixed Percentages (QQI)
        • Mixed Percentages (10QQI)
        • Mixed Percentages (QQI Count Down)
        • Mixed Percentages (QQI Relay)
        • Mixed Percentages (QQI BINGO)
        • Mixed Percentages (QQI Worksheets)
    • Factors and Multiples >
      • Number Properties (QQI)
      • Product of Primes >
        • Product of Primes (QQI)
        • Product of Primes (10QQI)
        • Product of Primes (QQI Count Down)
        • Product of Primes (QQI Relay)
        • Product of Primes (QQI BINGO)
        • Product of Primes (QQI Worksheets)
      • HCF and LCM >
        • HCF and LCM (QQI)
        • HCF and LCM (10QQI)
        • HCF and LCM (QQI Count Down)
        • HCF and LCM (QQI Relay)
        • HCF and LCM (QQI BINGO)
        • HCF and LCM (QQI Worksheets)
        • HCF and LCM (Video)
      • 100 Square Multiples (QQI)
      • 100 Square Types of Numbers (QQI)
    • Standard Form >
      • Standard Form Conversions >
        • Standard Form Conversions (QQI)
        • Standard Form Conversions (10QQI)
        • Standard Form Conversions (QQI Count Down)
        • Standard Form Conversions (QQI Relay)
        • Standard Form Conversions (QQI BINGO)
        • Standard Form Conversions 2 (QQI BINGO)
        • Standard Form Conversions (QQI Worksheets)
      • Standard Form Arithmetic >
        • Standard Form Arithmetic (QQI)
        • Standard Form Arithmetic (10QQI)
        • Standard Form Arithmetic (QQI Count Down)
        • Standard Form Arithmetic (QQI Relay)
        • Standard Form Arithmetic (QQI BINGO)
        • Standard Form Arithmetic (QQI Worksheets)
    • Ratio and Proportion >
      • Ratio (Video)
    • Surds >
      • Surds Activities >
        • Surds (QQI)
        • Surds (10QQI)
        • Surds (QQI Count Down)
        • Surds (QQI Relay)
        • Surds (QQI BINGO)
        • Surds (QQI Worksheets)
  • Algebra
    • Algebraic Manipulation >
      • Collecting Like Terms >
        • Collecting Like Terms (QQI)
        • Collecting Like Terms (10QQI)
        • Collecting Like Terms (QQI Count Down)
        • Collecting Like Terms (QQI Relay)
        • Collecting Like Terms (QQI BINGO)
        • Collecting Like Terms (QQI Worksheets)
      • Expanding Single Brackets >
        • Expanding Single Brackets (QQI)
        • Expanding Single Brackets (10QQI)
        • Expanding Single Brackets (QQI Count Down)
        • Expanding Single Brackets (QQI Relay)
        • Expanding Single Brackets (QQI BINGO)
        • Expanding Single Brackets (QQI Worksheets)
      • Factorising >
        • Factorising (QQI)
        • Factorising (10QQI)
        • Factorising (QQI Count Down)
        • Factorising (QQI Relay)
        • Factorising (QQI BINGO)
        • Factorising (QQI Worksheets)
      • Expanding Quadratic Brackets >
        • Expanding Quadratic Brackets (QQI)
        • Expanding Quadratic Brackets (10QQI)
        • Expanding Quadratic Brackets (QQI Count Down)
        • Expanding Quadratic Brackets (QQI Relay)
        • Expanding Quadratic Brackets (QQI BINGO)
        • Expanding Quadratic Brackets (QQI Worksheets)
      • Factorising Quadratics >
        • Factorising Quadratics (QQI)
        • Factorising Quadratics (10QQI)
        • Factorising Quadratics (QQI Count Down)
        • Factorising Quadratics (QQI Relay)
        • Factorising Quadratics (QQI BINGO)
        • Factorising Quadratics (QQI Worksheets)
        • Factorising Quadratic Expressions (Video)
        • Factorising Four Term Expressions (Video)
      • Indices >
        • Indices (QQI)
        • Indices (10QQI)
        • Indices (QQI Count Down)
        • Indices (QQI Relay)
        • Indices (QQI BINGO)
        • Indices (QQI Worksheets)
      • Completing the Square >
        • Completing the Square (QQI)
        • Completing the Square (10QQI)
        • Completing the Square (QQI Count Down)
        • Completing the Square (QQI Relay)
        • Completing the Square (QQI BINGO)
        • Completing the Square 2 (QQI BINGO)
        • Completing the Square (QQI Worksheets)
      • Algebraic Fractions >
        • Simplifying Algebraic Fractions (Video)
        • Adding and Subtracting Algebraic Fractions (Video)
        • Multiplying and Dividing Algebraic Fractions (Video)
    • Coordinates >
      • Coordinates (GGB)
      • Coordinate Battleship First Quadrant (GGB)
      • Coordinate Battleship All Four Quadrants (GGB)
      • 3D Coordinates (AGG)
    • Equations >
      • Linear Equations >
        • Solving Linear Equations >
          • Solving Linear Equations (QQI)
          • Solving Linear Equations (10QQI)
          • Solving Linear Equations (QQI Count Down)
          • Solving Linear Equations (QQI Relay)
          • Solving Linear Equations (QQI BINGO)
          • Solving Linear Equations (QQI Worksheets)
        • Solving Equations with Algebraic Fractions (Video)
      • Quadratic Equations >
        • Solving Quadratic Equations >
          • Solving Quadratic Equations (QQI)
          • Solving Quadratic Equations (10QQI)
          • Solving Quadratic Equations (QQI Count Down)
          • Solving Quadratic Equations (QQI Relay)
          • Solving Quadratic Equations (QQI BINGO)
          • Solving Quadratic Equations (QQI Worksheets)
        • Solving Quadratic Equations by Factorising (Video)
        • The Quadratic Formula (Video)
        • Problems Involving Quadratic Equations (Video)
      • Simultaneous Equations >
        • Solving Simultaneous Equations >
          • Solving Simultaneous Equations (QQI)
          • Solving Simultaneous Equations (10QQI)
          • Solving Simultaneous Equations (QQI Count Down)
          • Solving Simultaneous Equations (QQI Relay)
          • Solving Simultaneous Equations (QQI Relay Fixed)
          • Solving Simultaneous Equations (QQI BINGO)
          • Solving Simultaneous Equations (QQI Worksheets)
        • Solving Simultaneous Equations Graphically (Video)
        • Simultaneous Equations by Substitution (Video)
        • Simultaneous Equations by Elimination (Video)
        • Simultaneous Equations - One Non-Linear (Video)
    • Sequences >
      • Sequences Activity (QQI)
      • Sequences Activities >
        • Sequences (QQI)
        • Sequences (10QQI)
        • Sequences (QQI Count Down)
        • Sequences (QQI Relay)
        • Sequences (QQI BINGO)
        • Sequences (QQI Worksheets)
      • Generating Sequences (Video)
      • General Term for Linear Sequences (Video)
      • Simple Quadratic Sequences (Video)
      • General Term for Quadratic Sequences (Video)
      • General Term for Cubic Sequences (Video)
      • Geometric Sequences (Video)
      • Common Differences (QQI)
    • Graphs >
      • Straight Line Graphs >
        • Drawing Straight Line Graphs (GGB)
        • Gradient of a Line (GGB)
        • Gradient of a Line 2 (GGB)
        • Parallel Lines (GGB)
        • Perpendicular Lines (GGB)
        • y = mx + c Activity (GGB)
        • Battleships 1 (AGG)
        • Battleships 2 (AGG)
        • Battleships 3 (AGG)
        • Find the Lines 1 (AGG)
        • Regions in Graphs (Video)
      • Non-Linear Graphs >
        • Drawing Curves (GGB)
        • Quadratic Graphs Activity (GGB)
        • Finding Quadratic Functions (Video)
      • Graphs with a Casio GDC (Video)
    • Graph Transformations >
      • Graph Transformations 1 (GGB)
      • Graph Transformations 2 (GGB)
      • Graph Transformations 3 (GGB)
      • Graph Transformations 4 (GGB)
      • Graph Transformations 5 (GGB)
      • Graph Transformations 6 (GGB)
    • Functions >
      • Functions Introductions (Video)
      • Function Graphs and Important Points (Video)
      • Solving Unfamiliar Equations Using Functions (Video)
      • Function Notation Revision (Video)
      • Composite Functions (Video)
      • Inverse Functions (Video)
  • Shape
    • Symmetry >
      • Reflection Symmetry >
        • Reflection Symmetry in Quadrilaterals (GGB)
        • Reflection Symmetry in Triangles (GGB)
        • Reflection Symmetry in Other Shapes (GGB)
      • Rotational Symmetry >
        • Rotational Symmetry in Quadrilaterals (GGB)
        • Rotational Symmetry in Triangles (GGB)
        • Rotational Symmetry in Other Shapes (GGB)
    • Area and Perimeter >
      • Polygons >
        • Perimeters (GGB)
        • Area of a Triangle (GGB)
        • Area of a Parallelogram (GGB)
        • Area of a Trapezium (GGB)
        • Area of Compound Shapes (GGB)
        • Perimeter and Area (GGB)
      • Circles >
        • Discovering Pi (GGB)
        • Circumference of a Circle (GGB)
        • Area of a Circle (GGB)
        • Running Tracks (GGB)
        • Circle Area Problem (GGB)
        • Circles and Squares (GGB)
      • Area (QQI)
      • Area (10QQI)
      • Tilted Squares (GGB)
      • Difference Between Two Squares (GGB)
    • Volume and Surface Area >
      • Volumes and Surface Areas (QQI)
      • Volumes and Surface Areas (10QQI)
    • Angles >
      • Guess the Angle (GGB)
      • Angles on a Straight Line (GGB)
      • Angles around a Point (GGB)
      • Angles in a Triangle (GGB)
      • Angles in a Quadrilateral (GGB)
      • Angles in a Regular Polygon (GGB)
      • Angles on Parallel Lines (GGB)
      • Striping Angles (GGB)
    • Transformations >
      • Reflection >
        • Reflections (GGB)
        • Reflection Challenge (GGB)
      • Rotation >
        • Rotations (GGB)
        • Rotation Challenge (GGB)
      • Translation >
        • Translations (GGB)
        • Translation Challenge (GGB)
      • Enlargement >
        • Enlargements (GGB)
        • Enlargement Challenge (GGB)
        • Other Scale Factors (GGB)
      • Challenges >
        • Which Transformation (GGB)
        • How Many Transformations (GGB)
        • Find Them All (AGG)
        • Ultimate Challenge (GGB)
      • Matrix Transformations (AGG)
    • Pythagoras Theorem >
      • Pythagoras Theorem Activities >
        • Pythagoras Theorem (QQI)
        • Pythagoras Theorem (10QQI)
        • Pythagoras Theorem (QQI Count Down)
        • Pythagoras Theorem (QQI Relay)
        • Pythagoras Theorem (QQI BINGO)
        • Pythagoras Theorem (QQI Worksheets)
      • Pythagoras Theorem (GGB)
      • Pythagorean Triples (GGB)
      • Pythagoras Proof (GGB)
      • Ladders up Walls (GGB)
      • Pythagoras in 3D (GGB)
      • Finding the Hypotenuse Example (Video)
      • Finding a Shorter Side Example (Video)
    • Trigonometry >
      • Right Angled Trigonometry >
        • Right Angled Trigonometry (QQI)
        • Right Angled Trigonometry (10QQI)
        • Right Angled Trigonometry (QQI Count Down)
        • Right Angled Trigonometry (QQI Relay)
        • Right Angled Trigonometry (QQI BINGO)
        • Right Angled Trigonometry (QQI Worksheets)
        • Discovering Trig Ratios (GGB)
        • Finding Lengths (GGB)
        • Finding Missing Lengths (Video)
        • Finding Missing Angles (Video)
      • Sine Rule (Video)
      • Cosine Rule (Video)
      • Sine and Cosine Rules (Video)
    • Circle Theorems >
      • Angle in the Centre vs Angle at the Circumference (GGB)
      • Angle at the Centre vs Angle at the Circumference (Video)
      • Angles in a Semicircle (GGB)
      • Angle in a Semicircle (Video)
      • Angles in Cyclic Quadrilaterals (GGB)
      • Angles in a Cyclic Quadrilateral (Video)
      • Angles in the Same Segment (GGB)
      • Angles in the Same Segment (Video)
      • Tangents (GGB)
      • Tangents (Video)
      • Alternate Segment Theorem (GGB)
      • Intersecting Tangents (GGB)
      • Intersecting Tangents (Video)
      • Intersecting Chords (GGB)
    • Vectors >
      • Vectors and Scalars (Video)
      • Vector Notation (Video)
      • Resultant Vectors (Video)
      • Resultants of Column Vectors (Video)
      • Scalar Multiplication (Video)
      • Magnitude of a Vector (Video)
    • Miscellaneous >
      • Squares (GGB)
      • Tangrams (GGB)
      • Euler Line (GGB)
      • Geoboards
  • Statistics
    • Probability >
      • Probability (QQI)
      • Probability (10QQI)
      • Probability Tools (Flash)
    • Averages >
      • Averages Activity (QQI)
      • Listed Averages >
        • Listed Averages (QQI)
        • Listed Averages (10QQI)
        • Listed Averages (QQI Count Down)
        • Listed Averages (QQI Relay)
        • Listed Averages (QQI BINGO)
        • Listed Averages (QQI Worksheets)
        • Averages From Lists of Data (Video)
        • Quartiles and Interquartile Range (Video)
      • Averages from Frequency Tables >
        • Averages from Frequency Tables (QQI)
        • Averages from Frequency Tables (10QQI)
        • Averages from Frequency Tables (QQI Count Down)
        • Averages from Frequency Tables (QQI Relay)
        • Averages from Frequency Tables (QQI BINGO)
        • Averages from Frequency Tables (QQI Worksheets)
        • Averages From Frequency Tables (Video)
        • Averages From Grouped Frequency Tables (Video)
      • Averages With A GDC (Video)
    • Statistical Diagrams >
      • Cumulative Frequency (Video)
      • Scatter Graphs and the Mean Point (Video)
      • Scatter Graphs and Linear Regression on a GDC (Video)
      • Correlation and the Correlation Coefficient on a GDC (Video)
  • Post 16 Topics
    • Binomial Expansion >
      • Binomial Expansion (Video)
      • Binomial Theorem (Video)
      • Binomial Coefficients (Video)
      • Binomial Applications (Video)
    • Coordinate Geometry >
      • Coordinate Geometry (QQI)
      • Coordinate Geometry (10QQI)
      • Equation of a Circle (AGG)
    • Differentiation >
      • Differentiating Polynomials >
        • Differentiating Polynomials (QQI)
        • Differentiating Polynomials (10QQI)
        • Differentiating Polynomials (QQI Count Down)
        • Differentiating Polynomials (QQI Relay)
        • Differentiating Polynomials (QQI BINGO)
        • Differentiating Polynomials (QQI Worksheets)
      • Finding Gradients of Curves (QQI)
      • Finding Gradients of Curves (10QQI)
      • Finding Turning Points of Curves (QQI)
      • Finding Turning Points of Curves (10QQI)
    • Trigonometry >
      • Radian and Degree Conversions >
        • Radian and Degree Conversions (QQI)
        • Radian and Degree Conversions (10QQI)
        • Radian and Degree Conversions (QQI Count Down)
        • Radian and Degree Conversions (QQI Relay)
        • Radian and Degree Conversions (QQI BINGO)
        • Radian and Degree Conversions (QQI Worksheets)
      • Trigonometric Exact Values >
        • Trigonometric Exact Values (QQI)
        • Trigonometric Exact Values (10QQI)
        • Trigonometric Exact Values (QQI Count Down)
        • Trigonometric Exact Values (QQI Relay)
        • Trigonometric Exact Values (QQI BINGO)
        • Trigonometric Exact Values (QQI Worksheets)
      • Graphs of Trig Functions (GGB)
  • Starters, Puzzles and Enrichment
    • UKMT Random Question Generator
    • @mathschallenge Random Questions
    • School of Hard Sums Random Questions
    • Random Starter of the Day
    • Mathematically Possible (QQI Starter)
    • Adding Challenge (QQI Starter)
    • Date Starter (QQI Starter)
    • Name That Number (QQI Starter)
    • Matchstick Random Questions
    • Choose 3 Numbers (QQI Starter)
    • What's The Question (QQI Starter)
    • Mathematical Words (QQI Starter)
    • Number of the Day (QQI Starter)
    • Anagrams and Missing Vowels (QQI Starter)
    • Missing Vowels and Word Jumbles (QQI) >
      • Missing Vowels and Word Jumbles Simple Numbers (QQI)
    • Tables (QQI)
    • Target Boards (QQI)
    • Missing Signs (QQI)
    • Random Activities >
      • Exploding Dots
      • Easter Date
      • Easter Tangrams (GGB)
      • Zeller's Algorithm
      • Batman Equation (AGG)
      • Templates
    • Mathematical Videos >
      • Fermat's Last Theorem (Video)
      • Pi Song (Video)
      • Monty Hall Problem (Video)
      • Symmetry, Reality's Riddle (Video)
      • Music of the Primes (Video)
      • Folding Paper (Video)
      • Nature by Numbers (Video)
      • Inspirations (Video)

Aspects of Teaching

29/6/2020

0 Comments

 
I have been working on what I call the Aspects of Teaching, which is designed to underpin our Instructional Coaching Programme. The purpose behind this is to give coaches and teachers some broad areas of what we do to talk about, but also split it up a little bit to direct conversations to the most important parts that teachers want to work on.
Below is the Aspects of Teaching. It should start automatically, and takes about a minute to play through the whole animation. There is a static image version here.
Picture
Hopefully it is fairly self explanatory, which is why I have produced it in an animation form. But by splitting what we do into the 4 big Aspects, and then focusing on a particular detail within one of these, I am hoping to help create useful conversations.
For each Aspect there will be a set of strategies taken from various sources, including
  • High-Impact Instruction by Jim Knight
  • Teach Like a Champion 2.0 by Doug Lemov
  • Making Every Lesson Count by Shaun Allison and Andy Tharby
  • Teaching WalkThrus by Tom Sherrington and Oliver Caviglioli
These strategies will be used in the instructional coaching process as possible ideas that teachers could try to meet their goals. The next step of the process is to put these strategies together, and share them with the coaches so they can start to become experts in them.
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Compendium of Mathematical Methods

7/6/2020

1 Comment

 
I have just finished reading A Compendium of Mathematical Methods by Jo Morgan. It is a book directed at Maths teachers and has a simple purpose: sharing different methods that are used to perform some common processes that we teach.
For each of 19 topics, spanning the whole of secondary maths, Jo goes into depth on a variety of methods, always using 2 well chosen examples to show some of the subtleties you might otherwise miss. Accompanying this are some of her own notes, and excerpts from historical textbooks to show how these were approached in the past.
Jo stays neutral throughout the book, never saying one method is the best, but rather  presenting them as they are. A few concerns about some methods which rely on following a procedure rather than developing understanding are raised, but not in a judgemental way. The tone throughout is one of trying to start a conversation about mathematical methods.
When we come out of lockdown, I am going to take some of the chapters to my department to discuss. I think it is a great idea to talk about the merits of different methods, and looking at ones we don't use will help teachers develop their own subject knowledge too. I am also a fan of being consistent across the department in the main method we teach. I think this has benefits when students change teachers, and allows for more continuity. As we are a 3-18 all through school, we could even extend this to the primary school to discuss how we teach the foundation skills.
In terms of sharing methods with students, it is also nice to have a few other methods "up your sleeve" for those situations when they do not understand the primary one you use. Or with those who need an extra push, asking them to see if they can understand why different methods are actually the same can push their understanding. Perhaps using a method comparison example like Emma McCrea discusses in Making Every Maths Lesson Count could be used.
One thing that the book has made very clear to me is that we need to move to an area model of multiplication. It is a versatile and easy to understand method for multiplication, that can easily be extended to more complex topics such as algebraic expansion and factorising. I will be taking this to our department soon as I think this is something we should be consistent about.
It is a great read for any Maths teacher. It is not something that you need to read in one go, and perhaps is better read by chapter when you want to look at a particular topic.
And I am with Jo. Let's talk about methods. 
1 Comment

Just what is student engagement?

5/6/2020

0 Comments

 
I am writing this as we are in the middle of the global Covid-19 pandemic. This has shut schools across the globe, leaving most children to be taught remotely. I have blogged before about how I have used Online Live Teaching in this situation. 
But one of the things that seems to be on everybody's mind is how do we get students to engage in this type of teaching. Without having students in the class it is much more difficult to judge engagement, and for some it is even difficult to ensure they are present and doing the work.
This raises the debate over what we actually mean when we talk about engaging students. As a younger teacher, I firmly fell into the camp of believing that lessons should be fun in order to motivate students to be engaged in lessons. I would spend hours designing activities, be it card sorts, bingos or jigsaw activities to keep the students busy and active throughout the lesson. My thinking behind this was that if they were kept busy, then they would be engaged in the lesson. 
Well, if I am being honest, I do not really mean "my thinking" in that last sentence. I mean "I was told/led to believe". Not necessarily directly, but certainly through the types of activities we were shown in my teacher training. These were the activities that were modelled to us, and so these were the types of activities that we employed in our teaching. And it was all about that holy grail of education: student engagement.
For those first few years of my career my job was to engage the students in the lesson, usually by making it fun in some way. Perhaps that was through the way I "performed", or through the activities I prepared. But my main concern was that students enjoyed lessons.
But now I see things differently. 
I still believe in engagement. We know from plenty of research that it is vital that students are engaged with the learning in order to learn the material (for example, check out MARGE by Shimamura). But there is a subtle but important difference in the language. You may not have noticed it.
At the start of this post I referred to students being engaged in the lesson. Now I am saying that students are engaged with the learning. 
And that is the crux of the issue when it comes to discussing engagement. Is our job to create engaging (fun) lessons? Or is it to make the content that students need to learn engaging? These are very different things. You could argue that the former is easier (though the workload was killer!) in that it requires far less thought on everybody's part. But again, that is the problem. As Willingham says, "memory is the residue of thought", and if we want students to remember things, we have to get them to think deeply about those things. And interestingly, this normally piques their interest and gets them engaged in the lesson.
So in this time of remote teaching when we are all concerned about keeping students engaged in their school work, think about this: do you want students to have fun, or do you want them to learn something? If it is the latter, perhaps you would be better off thinking hard about the content you want them to know, and, more importantly, how you can get the students to think really hard about it. Engage them in the learning, and they will be engaged in the lesson.
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    Dan Rodriguez-Clark

    I am a maths teacher looking to share good ideas for use in the classroom, with a current interest in integrating educational research into my practice.

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