WHY IS MATH TAUGHT DIFFERENTLY ?

Who is in the room? 1. Parent/Teacher/Caregiver of….(grade levels) 2. School district (county or independent)

 How many of you LOVE math?  Math was your FAVORITE subject…  Are you confident in your mathematical thinking?

Why do we care about how math is taught?

Elementary Standard:  Please do not blurt your response.  Add (without paper)

Number Talk in Action: Grade 3

What do the standards say? Grade 3 Math Standard Number and Operations in Base Ten (3.NBT) Use place value understanding and properties of operations to perform multi-digit arithmetic. 1. Use place value understanding to round whole numbers to the nearest 10 or Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction.

When does math stop making sense? fractions Long Division

What do you remember about fractions? Make a list at your table of what you know about fractions…and what you remember learning about fractions

Kentucky Department of Education 10 Try this problem: Estimate the answer: 12 / / 8 A) 1 B) 2 C) 19 D) 21 E) I don’t know.

Kentucky Department of Education 11 National Assessment of Educational Progress (NAEP) results show an apparent lack of understanding of fractions by 9, 13, and 17 yr olds. Estimate the answer: 12 / / 8  Only 24% of the 13-yr-olds responding chose the correct answer, “2”.  55% selected 19 or 21  These students are operating on the fractions without any understanding of the math. Results from the 2 nd Mathematical Assessment of the National Assessment of Educational Progress

Children’s Ideas about Fractions:  Show me where ½ could be on the number line below: Kentucky Department of Education Why do students sometimes choose this part of the number line?

Children’s Ideas about Whole Numbers:  3 > 2 ALWAYS.  1 = 1 ALWAYS.  So…how can it be that 1 / 3 > ½ ? Kentucky Department of Education 13

When students can’t ‘remember’ a procedure, they resort to performing any operation they know they can do… Estimate the answer: 12 / / 8 A) 1 B) 2 C) 19 D) 21 E) I don’t know. Kentucky Department of Education 14

…instead of making sense of the numbers they are attempting to add. Kentucky Department of Education 15

Perhaps you’ve seen this reasoning… 1 / / 3 = 2 / 5  If students have an understanding of the value of the fractions on a number line, or as parts of a whole, then they can argue the unreasonableness of this answer. Kentucky Department of Education 16

FRACTION MANIPULATIVES Kentucky Department of Education 17

Learning Activity: Fraction Circles The white circle is 1. What is the value of each of these pieces? 1 yellow 3 reds 1 purple 3 greens Kentucky Department of Education 18 Now…change the unit: The yellow piece is 1. What is the value of those pieces?

Learning Activity: Using Counters Eight counters equal 1, or 1 whole. What is the value of each set of counters?  1 counter  2 counters  4 counters  6 counters  12 counters Kentucky Department of Education 19 Now, change the unit: Four counters equal 1. What is the value of each set of counters?

Learning Activity: Number Lines Kentucky Department of Education 20

Confusing Procedures…  2/3 x 1/2

GradeRequired Fluency K Add/subtract within 5 1 Add/subtract within 10 2 Add/subtract within 20 (mental strategies) Add/subtract within 100 (strategies) 3 Multiply/divide within 100 (strategies) Add/subtract within 1,000 (strategies) 4 Add/Subtract multidigit whole numbers (standard algorithm) 5 Multidigit multiplication (standard algorithm)

 Ways to think and talk about math  Learn different ways to approach problems by asking questions  Look for patterns  Use different tools strategically  Students find many paths to the right answer.  Students learn to compare and collaborate with their peers and teacher to make sense of what they are learning and apply it in creative, real world ways.

 Explain their thinking  Work well with others  Be resourceful when new or unknown problems arise  Not “because my teacher told me to do it this way, Instead “let me explain it to you in my own words”

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