Building Math Confidence Ann-Marie Hunter Reasons for Building Math Confidence Math skills are often...

Building Math Confidence

Ann-Marie Hunter

Reasons for Building Math Confidence

Math skills are often seen as a source of anxiety; students are sometimes made to feel that they are destined to fail.

Your efforts to reduce Math anxiety can alter their attitudes towards their own abilities and create success for students.

Connecting to the learners in your classroom is one of the most important aspects of teaching – it conveys to the learners that they can trust you and that you believe they can succeed.

Focussing on creating a learning environment that is meaningful to the learner, allowing him/her to explore topics with confidence, supports the creation of a positive learning environment. You can use Math teaching to reach this goal!

“I had a great feeling of relief when I began to understand that a youngster needs more than just subject matter. 

Oh, I know mathematics well, and I teach it well.  I used to think that that was all I needed to do. 

Now I teach children, not math.  I accept the fact that I can only succeed partially with some of them. 

I have found further that my own personhood has educatable value.  When I don’t have to know all the answers I seem to have more answers than before, when I tried to be the expert. 

The youngster who really made me understand this was Eddie.  I asked him one day why he thought he was doing so much better than last year. 

He gave meaning to my whole new orientation. “It’s because I like myself now when I’m with you,” he said.”    

~ a quote from a teacher                                                                                                     

Words of Wisdom

Workshop Outline

Use Brain Research to Sharpen Your Teaching

Semantic memory People can say “The Earth is the third planet from the sun”, without having

any specific experience in going to space to see that the Earth is in that position.

Episodic memory A person may remember a recent trip to Paris, mentally reliving events that

happened there, in the mind’s eye seeing again the places visited, sights seen, sounds heard, aromas smelled, and people met.

Procedural memory Driving a standard vehicle or riding a bike is an example of use of

procedural memory.

Adjust your teaching in these ways:Personalize instruction to promote retention

Use visual tools for learning

Verbally reinforce learning as much as possible

Use hands-on materials as much as possible

Incorporate movement within each lesson

If Joe and his brother were playing basketball outside and Joe took three times as many shots as his brother, how

many shots could Joe have taken if they took no more than 40 shots in total.

1) Teach Word Question Vocabulary. (In your handout)Word Question Vocabulary

sum - the answer when you add numbers.difference - the answer when you subtract

numbers.product - the answer when you multiply numbers.quotient - the answer when you divide numbers.total - the amount that is gained by the addition of

smaller amounts.

Word Question Vocabulary

2) Have students create word questions BEFORE they are asked to answer textbook questions.

Give choices in their word question challengeExample:Word Question Criteria:

Use decimal numbers or fractions in your question.Use numbers that are either less than 20 or more than 50.Ensure that there is more than one correct answer to your question.

3) Guide your students with methods for solving word questions. (Find Word Question Strategies on the Wiki)Strategies to Find SolutionsGet Started - Record important details in an

organized fashionUse a Diagram to represent the parts of the

questionMake the question Simpler using Easier

NumbersGet Unstuck – try a different approach

4) Use the Place Mat Activity to celebrate and share students’ ideas.

Student #1 Work Space Student #2 Work Space

Student #3 Work Space Student #4 Work Space

This is where the word question is written.

Post finished Place Mats to celebrate diversity of solutions.

2) Place Value – Reading numbers ____ “hundred” ____ “tee” ____ then say the final digit. Example: 572 reads as: 5 hundred, 7 tee, two. Read any number:

__ __ __ MILLION __ __ __THOUSAND __ __ __ . __ tenths

and

__ __ __ MILLION __ __ __THOUSAND __ __ __ . __ __ hundredths

and

Write numbers in words:67 893 542Sixty-seven MILLION, eight hundred ninety-three

THOUSAND, five hundred forty-two

3) Focus on the Facts “After learning to read, learning the

multiplication facts is probably one of the most important things we learn in elementary school.” - Trevor Calkins

We sometimes do not give the needed attention to this part of Math instruction, thinking that “we have all those units to cover!”

The truth is that helping a child to learn and understand the basic facts is one of the best ways to build confidence!

After he/she knows the facts, everything seems easier – and IS easier! His/her Mental Math skills begin to develop.

Knowing Math facts allows students to confidently engage in learning new concepts.

Ensure that students can add and subtract numbers using a visual tool – Power of Ten cards are so valuable in developing these vital skills.

Ex: 7 + 8 = (5 + 2) + (5 + 3), = (5 + 5) + (2 + 3), = 10 + 5, = 15 Let’s Try This!

Eventually, they will ‘see’ these relationships in their heads without using the cards.

Use Visual Tools to reinforce the meaning of multiplication and division:

Power of Ten multiples sheet – visually shows groups of numbers Look in your handout for this page!

6 X 7 = 5, 10, 15, 20, 25, 30 (skip counting the first columns)

(adding on the twos) 32, 34, 36, 38, 40, 42

Other ways to represent multiplication factsCross lines: Arrays:Count the intersections. Shade a section of graph paper.

3 X 9 = 27 3 X 7 = 21

Record the total for each line. Record the total for each row.

Talk about multiples as ‘groups of #’ – to encourage the visual

3 X 2 means 3 groups of 2:

4 X 7 = 28, so 7 X 4 = 28, 28/7 = 4, and 28/4

= 7

Talk about multiplication and division together – Fact Families

Visually looks like half as many to learn Helps students to practise what they

know in an organized mannerUse the blank sheet on one side, with

answers on the other, to encourage pairs of students to study together

Teach Perfect Squares: 2 X 2, 3 X 3, 4 X 4 … and other patterns on the sheet

Reduced Times Tables sheet

Fantastic Factors sheetGiven the answer (24), the students are

challenged to find all the ‘questions’ – the factor pairs

Students can first list all the numbers that divide evenly into the number - use divisibility rules

1, 2, 3, 4, 6, 8, 12, 24 Then use ‘RAINBOWS’ to link 1 X 24 up the pairs: 2 X 12 3 X 8 Let’s practise this! 4 X 6

Divisibility Rules – to find factorsA number is evenly divisible by:

2, if the number ends in a 0, 2, 4, 6, or 8 (the number is an even number)

3, if the digital sum is a 3, 6 or 9 (add all the digits of the number to get the digital sum)

5, if the last digit of the number is a 5 or a 0

Arrow Graphs – * offer opportunity for students to think

creatively * demonstrate student understanding

4 8 - 4

1 + 1 + 1 + 1

16/4

300 - 296

(2 X 7) – (5 + 5)

½ + ½ + ½ + ½ + ½ + ½ + ½ + ½

9.5 – 4.1 – 1.4

40 000 divided by 10 000

LEARNING FACTS – Such an Important Part of Math Instruction!

This aspect of your Math instruction cannot be overestimated!

You are doing your students such a tremendous service by focussing on learning facts in a meaningful way and ensuring that they have solid knowledge of the facts when they leave your classroom.

Additional Resources to make learning fun:

Timestables the Fun Way! - Judy Rodriguez Contextual representation of

the multiplication facts. Example 1: • Sean climbs to the top of the hill to fly his kite.• He’s so happy when he turns 16 and gets his driver’s license, • because then he can drive his 4 X 4 to the top of the hill. Remember: You need to be 16 to drive a 4 X 4, so

4 X 4 = 16! Example 2: 6 X 6 – Oasis in a desert.

4) Mental Math/estimating skillsModel Mental Math: Talk about how you

do calculations in your head, without writing anything on paper – ask students to share their methods of doing the same.

Encourage the use of visual tools to support Mental Math. Share how the students’ thinking will improve when they can ‘see’ the numbers in their heads.

Estimating answers to questions before calculations are done• Use Vertical Number Lines to aid in Visualizing closest ten, hundred, whole number (decimal vertical number line). Check your handout!

• Estimation allows students to be able to predict the approximate answer before using the calculator.

• Canada’s recent phasing out of the use of pennies is a real life situation requiring rounding to the nearest 5.

Practise multiplying by powers of 10

3 X 10 = 30 7 X 100 = 700 2 X 1000 = 2 000 40 X 300 = (4 X 3) = 12 then place the number of

zeros in the question (3 zeros) behind the 12 to get 12 000.

200 X 500 = (2 X 5) = 10, then place the 4 zeros behind the 10. Answer: 100 000

Partners challenge each other and check answers on calculators.

Motivate students with Mental Math Tricks

1) Multiplying any 2-digit number by 11:

34 X 11 4 7 3 374

•The final digit of the answer is the final digit of the original number

•The middle digit of the answer is the sum of the two digits of the original number (3 + 4)

•The first digit of the answer is the first digit of the original number (plus any carried ten from the sum of the two digits).

2) Squaring any 2-digit numbers that end in a 5:

Multiply the first digit times one higher and finish the number with ‘25’

Example: To square 75 (finding 75 X 75) Use ‘7’, and multiply 7 X (7 + 1) = 7 X

8 = 56, then place ‘25’ on the end: 5625. 75 X 75 = 5625

3) Adding and Subtracting from Left to Right

46 + 36 = (40 + 30 = 70), (6 + 6 = 12), so the answer is 70 + 12, which is (70 + 10) + 2, or

= 80 + 2 = 82 95 – 33 = (90 – 30) + (5 – 3) = 60 + 2 = 62 Let’s Try This Encourage students to share their own

methods for using Mental Math

4) Multiplying from Left to Right:

25 X 32 = (25 X 30) + (25 X 2) = = (25 X 3 X 10) + 50 = (75 X 10) + 50 = 750 + 50 = 800 Encourage students to share their own

methodsLet’s try this!

5) Fractions & Decimals Demystified

5) Fractions & Decimals DemystifiedThe Family Math Fraction Kit is a wonderful game – I

suggest that it be played with decimal names included.

Ratios and Percent will be an easy transition from this understanding.

Use Factoring skills to develop confidence with writing equivalent fractions and simplifying fractions.

Let’s Try This!

= 53 hundredths = 53 %

6) Mastering the Basics Benefits of using the Mastering the Basics

program Strategies for running the program

successfully

7) Geometry & MeasurementUse measurement often throughout

year Discuss polygons and their namesBuild Geometric 3-D figures Classify triangles and quadrilaterals‘Regular’ polygons - equal side lengthsUse terms: Perimeter, Area, and

Volume and the related Measurement skills throughout the year

Use specific definitions:Perimeter: distance along the outline of a figureArea: number of square units inside the outline of a

figureVolume: space inside a solidClarify units used for each of these measurements

Hands-on recording of lengthVisual tool for Metric Conversion (Check handout).Clarify the difference between prisms and pyramids

(Check handout)

7) Geometry & Measurement

8) Games and TricksYou cannot overestimate the power of

play! Uses Episodic MemoryJournals enrich learningFamily Math Games are great!Power of Ten games – super!Let’s try out a mental math game!

Additional Strategies & Ideas for building your own Math confidencePlease take a moment to read over the guidelines

for Math teaching – highlight those that you think would be helpful for you to try out.

Let me know if you would appreciate clarification of any of the strategies listed.

Let’s talk about how you can improve your own Math confidence

Decide which of these ideas you think you can follow right now – make a plan to do that!

Power of Ten WebsitePower of Ten program – confidence building resourceDevised by Trevor Calkins – Victoria BC

educatorVideos very helpful for early career teachers20% discount when you email Trevor

and mention Ann-Marie’s workshop

Please join PITA ~Provincial Intermediate Teachers AssociationIt’s only $15 to join PITA if you are a TTOC,

student, or teacher without a position. Attending a PITA workshop automatically makes you a member!

pita.ca – lots of resources on the Wiki and information about upcoming events.

PITA Facebook page with links to cool stuffnewsletters with great teaching ideas 3 times a

yearamazing PSA – with a focus on providing great

PD

Start UP! Your Class Workshopsstartupyourclass.ning.com – is the Start UP!

website. Part of PITA! focussed on early career teacherscontains links to resourcesblogs and info about upcoming eventsLate August workshops - practical Unit Strategies in all subject areasopportunities to connect with presenters and discuss your trials with new

materials

Thank you for being a teacher!