Instrumentation in Mathematics

Topics: Problem solving, Orders of magnitude, Angle Pages: 41 (8575 words) Published: January 7, 2013

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Title Pagei
Table of Contentsii-v
Theoretical Considerations, Literature and Research Studies on the Use of Learning Aids 1-16
Activity Sheets17
On Numbers
Complete the Skip Counting Series18-19
On Measurement
Metric Length20
Metric Weight21
Metric Capacity22
Compare Metric Measurements23
Metric System Measurement Conversions24
Reading a Tape Measure25
Reading a Decimal Ruler26
Reading a Metric Ruler27
Reading a Standard Ruler28
Measuring in Inches29
Measuring in Centimeters30
Converting Feet to Inches31
Converting Fahrenheit to Celsius32
Find the Temperature for each Thermometer
in Degree Celsius33
What is the reading in milliliters for each
graduated cylinder?34
Liquid Measure Quiz35
Conversion Factors36
Converting English to Metric37
On Algebra
Identify the Properties of Mathematics38
Working with Properties of Mathematics39
Prime factors of the Numbers40-41
Greatest Common Factor43
Exponents 44-46
Radicals 47
Scientific Notation 48
Adding Fractions50-53
Subtracting Fractions54-56
Multiplying Fractions57-59
Dividing Fractions60-62
Equivalent Fractions63
Reducing Fractions64
Converting of Fractions65
Comparing Fractions66
Order of Operations67-68
On Geometry
Classifying Angles71
Naming Angles and Vertices72
Naming Relationships of Angles73
Finding Measures of Angles74
Angle Measure75
Drawing Angles76
Points in an Angle77
Find the missing angle measurement
using the angle addition postulate78
Find the missing angle measurement in each
set of complementary angles79
Find the missing angle measurement in each
set of supplementary angles80
Find the missing vertical angles81
Find the missing alternate angles82
Find the missing corresponding angles83
On Trigonometry
Find the length of the third side of each triangle84
Find the distance between the points85-86
On Statistics
Arrange in Ascending Order and Find the Range89
Finding the Mean of a Data Set90
Calculating the Mean, Median, Mode and Range91
Calculating Mode92
Calculating the median of a Data Set93
Calculate the first, second, and third quartile
for each Data Set95
On Probability
Determining the Probability96
Choice based Probability97
Spinner Probability with Critical Thinking98
Graphing Calculator99-100

Research studies have evaluated the effectiveness of manipulatives as a tool in mathematics instruction. One line of research has studied the Concrete-Representational-Abstract (CRA) sequence of instruction, a form of explicit instruction that moves students from concrete manipulatives to pictorial representations of those manipulatives and finally to abstract concepts. Butler, Miller, Crehan, Babbitt, & Pierce (2003) compared the effectiveness of teaching fraction concepts to students with learning disabilities using a CRA approach versus a Representational-Abstract (RA) approach (starting with pictorial representations and moving to abstract concepts, with no concrete manipulatives). Fifty middle school students with mild to moderate disabilities were assigned to the CRA or the RA group. While both groups improved their understanding of fractions, the CRA group had overall higher scores than the RA group. A study by Witzel, Mercer, & Miller (2003) also supports the...
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