Download presentation
Presentation is loading. Please wait.
1
1 NCSM 2008 Dr. Eric Milou Rowan University Department of Mathematics milou@rowan.edu 856-256-4500 x3876 Conceptual Understanding and Basic Skills: Discussion Points for Teachers and Parents
2
2 Overview National Math Panel Recommendations Conceptual vs. Procedural Debate Number Sense & Computation Proficiency
3
3 National Math Panel (NMP) A focused, coherent progression of mathematics learning, with an emphasis on proficiency with key topics, should become the norm in elementary and middle school mathematics curricula. Any approach that continually revisits topics year after year without closure is to be avoided.
4
4 NMP Instructional practice should be informed by high-quality research, when available, and by the best professional judgment and experience of accomplished classroom teachers. High-quality research does not support the contention that instruction should be either entirely “student centered” or “teacher directed.”
5
5 NMP A major goal for K–8 mathematics education should be proficiency with fractions (including decimals, percents, and negative fractions).
6
6 Response (Gary Stager) The Report of the National Mathematics Advisory Panel does not dispute that teachers spend lots of time teaching fractions. The report merely urges that teachers do even more of the same while hoping for a different result. A definition of insanity comes to mind. It would be bad enough if wasted time was the only consequence of the fanatical fraction focus, but too many students get the idea that they can’t do math. This damages their inclination towards learning other forms of mathematics. Given the importance of mathematics and the widespread mathphobia sweeping the land, students can ill afford to a diminution in their self-image as capable mathematicians.
7
7 Response (Peanuts)
8
8 Education Week 11/1/06 We cannot afford to waste time on polarization. What is important is that we pragmatically address critical target areas to improve mathematics education. We cannot be distracted from our primary mission—to match tactical initiatives in other, newly technological societies that are snatching our competitive advantage in innovation—while we bicker over modest differences in approach. (Jere Confrey)
9
9 Compute the following: 4 x 9 x 25 How many ounces are in a gallon? 4 x 4 ÷ 4 x 4 30 ÷ 3/4
10
10 What’s “Typical?” in US
11
11 Third International Math & Science Study (TIMSS) Procedures vs. Concepts
12
12 Stated vs Developed
13
13 We need a BALANCE Balance Direct Instruction Constructivism Balance Conceptual Understanding Algorithmic Proficiency These are NOT Dichotomous
14
14 Conceptual Understanding 24 ÷ 4 = 6 24 ÷ 3 = 8 24 ÷ 2 =12 24 ÷ 1 = 24 24 ÷ 1/2 = ??
15
15 Fractions - Conceptually More than 1 or Less than 1 Explain your reasoning The F word
16
16 Which is larger? (2/3 + 3/4 + 4/5 + 5/6) OR 4 12.5 x 45 OR 4.5 x 125 (1/3 + 2/4 + 2/4 + 5/11) OR 2
17
17 Conceptual Fraction task Kim’s teacher asked her class to design a flag using four colors, dividing a square into parts, and to color the parts as follows: 1/2 is colored red 1/4 is colored blue 1/8 is colored green Any other part is to be left white
18
18 Flags
19
19 Harder Task A chocolate bar is separated into several equal pieces. If Laura eats 1/4 of the pieces; and Paul eats 1/2 of the remaining pieces; There are six pieces left over Into how many pieces was the original bar divided?
20
20 Chocolate Bar LAURA P A U L 16 pieces
21
21 Decimals 1000 ÷ 1.49 = 671.1409396 = Torture! Big Macs Sell for $1.49, how many Big Macs can I buy for $10.00? 1 is $1.50 2 are $3 4 are $6 6 are $9 Mental Mathematics is a vital skill 1.491000
22
22 Computation is Important Engaging & Active Less passive worksheets More thinking & reasoning
23
23 Numbers Are Everywhere
24
24 Computational Practice Target #: 6 3 8 17 1 3
25
25 Active Computation Fifty (1, 2, 3, 4, 5, 6 and addition) Buzz (3) Product Game
26
26 Conceptual & Contextual 8 + 7 = ? How do we teach this? xxx x xx x x x x x x x x x x x
27
27 8 + 7 = ? 2 5 10 + 5 = 15
28
28 17 - 8 = 1 7 - 8 / / 0 17 2 7 8 --> --> 10 --> --> --> --> --> --> --> 17
29
29 How Many Circles? 50
30
30 1000 - 279 = ? 279+1 = 280+ 20 = 300+700 = 1000
31
31 1000 - 279 = ? 1000 - 1 = 999 999 -278 721
32
32 Multiplication 13 x 17 = ? 1 3 x 1 7 1 2 9 031 2 2 1 ------- 10 7 10 3 1 0 0 3 0 7 0 2 1 221
33
33 Conceptual approach leads to ? x 7 x3x3 x2x2 3x 7x 21 Algebra: (x + 3) (x + 7) =
34
34 Contextual Problem Solving ≠ More Word Problems
35
35 Example 1: Sneakers SECOND purchase Nike ConverseReebok Nike Converse Reebok FIRSTFIRST
36
36 100 Students 50 1st time Nike buyers 30 1st time Converse buyers 20 1st time Reebok buyers How many would buy Nike the second time? 50 x.4 + 30 x.2 + 20 x.1 = 28 NC R N C R
37
37 Example 2: Drug Steady State 10 mg Zrytec daily 50% of Zrytec is eliminated daily What % is in the body after 7 days 10 days n days?
38
38 10mg Daily of Zrytec DayMg. of Zyrtec 1 2 3 4 5 6 10 15 17.5 18.75 19.375 19.6875
39
39 Fact #1 A
40
40 Fact #2 B
41
41 Fact #3 C
42
42 Fact #4 D
43
43 Fact #5 E
44
44 Fact #6 F
45
45 Fact #7 G
46
46 Fact #8 H
47
47 Fact #9 I
48
48 What is this?
49
49 What is this? F A C E
50
50 What If? AB C DE F GH I
51
51 Try Again
52
52 Try Again D E C A D E
53
53 What’s the Point? Isolated Facts Less likely to retain information Connected Facts, Patterns, Facts in Context More likely to retain information
54
54 Characteristics of a good mathematics program CONCEPTUAL CONTEXTUAL CONSTRUCTIVISM COMPUTATION
55
55 Thank You Dr. Eric Milou Rowan University milou@rowan.edu http://www.rowan.edu/colleges/las/departments/math/facultystaff/milou/eric.html
Similar presentations
© 2025 SlidePlayer.com. Inc.
All rights reserved.