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 Get all terms to one side, to solve a quadratic FACTOR Solve a 2-step equation (subtract, then divide) Check for extraneous solutions
If they can’t distribute, how can you know whether or not they can solve -5x+14=0? They won’t get that far. FACTOR Find a common denominator and multiply Solve the NUMERATOR Distribute Combine like terms Get all terms to one side, to solve a quadratic FACTOR 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, to- do 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/algebra- touch/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
Strategy #3: Technology! 1.
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
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