19 Strategies to Banish Fear from Your Math Classroom Dr. Christina Holland, Marietta High School, Marietta, GA
Math is hard! It can t be faked or fudged Math builds on itself It s a moving target (common core vs other methods) Students are trained to fail, and to expect failure
What makes them sweat? Fear #1: Too many steps! (overwhelm) Fear #2: Word problems Fear #3: Graphing Fear #4: This problem isn t like the example Fear #5: Getting lost in the calculations
Fear #1: Too many steps! IEP Strength: In math, John does well at solving 1-2 step algebraic problems, and can be successful with multi-step problems when provided with similar examples to work from. IEP Need: John will often become lost on long multi-step mathematical processes and will need to be guided back on track to find the next step. He also struggles with retaining the concepts and processes from one class period to the next. IEP Goal: When given a worksheet of multi-step equations/inequalities with one variable, the student will independently solve the equation/inequality with 80% accuracy.
Fear #1: Too many steps! Avoid the wall of equations What looks like one problem is actually many problems Sample Problem:
Strategy #1: Break it down Strategy #2: Color coding Strategy #3: Flow chart, to-do list Strategy #4: Play to their strengths
The problem is the amount of expected work for one problem:
Skills required: FACTOR Find a common denominator and multiply Solve the NUMERATOR Distribute Combine like terms FACTOR Get all terms to one side, to solve a quadratic Solve a 2-step equation (subtract, then divide) Check for extraneous solutions
FACTOR Find a common denominator and multiply Solve the NUMERATOR Distribute Combine like terms FACTOR If they can t distribute, how can you know whether or not they can solve -5x+14=0? They won t get that far. Get all terms to one side, to solve a quadratic Solve a 2-step equation (subtract, then divide) Check for extraneous solutions
Strategy #1: Break the one problem into many, so students can show the parts they know, and you can tell where EXACTLY they need help.
Strategy #2: Color code the steps
Strategy #3: Flow Charts, todo lists, graphic organizers
Strategy #4: Play to their strengths Be ready to pivot the way you teach it Cheers and songs Hands-on (skittle algebra) Hands-on with Tech: http://nlvm.usu.edu/en/nav/category_g_4_t_2.html (google NVLM : National Library of Virtual Manipulatives)
Strategy #4: Play to their strengths More Hands-on: https://itunes.apple.com/us/app/algebratouch/id384354262?mt=8 Algebra Touch app for iphone and ipad
Fear #2: Word problems Strategy #1: Teach the math vocabulary.
Fear #2: Word problems Strategy #2: Avoid the wall of text! Separate out the sentences Bold, underline, font size Break things up visually Identify the actual QUESTION.
Ansley takes twice as many hours to clean the garage as her sister Betsy. When they both work together, they can clean the garage in 6 hours. How many hours would it take Betsy to clean the garage alone?
How many hours would it take Betsy to clean the garage alone? (x=number of hours for Betsy alone) Ansley takes twice as many hours to clean the garage as her sister Betsy. (2x) When they both work together, they can clean the garage in 6 hours.
Strategy #3: Give the form of the equation(s) Strategy #4: Color code to map the words to the equation How many hours would it take Betsy to clean the garage alone? (x=number of hours for Betsy alone) Ansley takes twice as many hours to clean the garage as her sister Betsy. (2x) When they both work together, they can clean the garage in 6 hours.
Strategy #5: Use more than just words! Ms. Lady s kindergarten class rented and filled 1 van and 2 buses with 29 people to go to the fair. The first grade classes at Westside Elementary rented and filled 3 vans and 4 buses with 63 people. Find the number of people in each van and in each bus. 1x + 2y = 29 3x + 4y = 63
Model drawing approach (Can also be done with counters and containers.) =29 =63
Model drawing approach (Can also be done with counters and containers.) =29 =63 29 = 34
Model drawing approach (Can also be done with counters and containers.) =29 =34 29 = 5 in each van
Model drawing approach 5 = 29 5 = 24 students in 2 buses Answer: 5 students in each van, and 12 students in each bus
Fear #3: Graphing We re not talking about this anymore: Or even this:
Now it s more like this: So how can we teach kids to handle complex graphing?
Why is graphing so hard? o X versus Y: Which is which? Why? o Decimals and negatives: I can put the point (3, 5) on the graph. But where do I put (-2.7, 6.4)?? o Arbitrary seeming rules: Graph dotted lines for the asymptotes. Then put points for the x and y intercepts, count up and over for the slope, put open circles for any holes o Vocabulary: x-intercept, y-intercept, asymptote, end behavior, slope, maximum, minimum, hole, open circle, domain, range,
Strategy #1: Break into steps Strategy #2: Color code vocabulary and steps
1. Strategy #3: Technology!
Strategy #3: Technology! 2. www.google.com
Strategy #3: Technology! 3. www.desmos.com/calculator Sliders show how the equation changes the graph
Fear #4: This problem isn t like the example
Fear #4: This problem isn t like the example Strategies: #1 Lots of examples #2 Discuss similarities and differences #3 Pick your battles #4 Color coding the steps #5 Have students explain to each other and the class
Fear #4: This problem isn t like the example Strategies #6: Games!
Fear #5: Getting lost in the calculations Where do decimals fit in? Understanding fractions vs. decimals Negative numbers Don t know number facts Recognizing when answers are reasonable, and not.
Getting lost in the calculations: Strategies Number lines Post them. Use them Actively teach number sense think aloud Use reference sheets (for multiplication tables, etc.) Technology (calculators)
What strategies can you use? Fear #1: Too many steps! (overwhelm) Fear #2: Word problems Fear #3: Graphing Fear #4: This problem isn t like the example Fear #5: Getting lost in the calculations