“Numeracy empowers people by giving them tools to think for themselves, to ask intelligent questions of experts, and to confront authority confidently” (Steen, 2001, p.2, as cited in Booker, Bond, Sparrow, & Swan 2010, p.1). Individuals require the ability to fluently recognise numbers, add, subtract, multiply, use measurement and statistics to use in everyday life or work, however due to a change in society we now rely on machines to carry out these tasks. This shift in society has meant a change in how mathematics is taught in schools. Learning Managers are required not only to teach the simple skills however to teach students to understand the thinking on a range of mathematical processes (Booker, et al., 2010, p.2). Students are required to learn how to use, communicate and make sense of mathematics in everyday practices. Numeracy now includes reading, writing, listening, speaking and critical thinking (Booker, et al., 2010, p.8). Theories of learning influence mathematics curricula, classroom practice and how we think children learn.
Measurement
Imminently hands-on yet elusively abstract, measurement skills and concepts can be engaging but challenging to teach. What can be measured? Time, energy, space, and matter. Each of these physical aspects of our world has its measurable aspects, their respective measurement tools, and units of measure (see Figure 1.7). Some textbooks and curriculum frameworks classify money as a measurement topic; however, money is not measured but counted (unless all quantification is considered a form of measurement). Measurement is a critical topic for other mathematics applications and is related to many other topics outside mathematics. Both customary (U.S.) and metric systems are referenced in the standards (the customary system reinforces fraction concepts and metrics reinforce the base-ten place value system and decimal concepts).
Measurement: Subject, Tools, and Units
| Category | Subject | Example Tool | Example Unit | |
| Time | long periods short periods shorter periods tempo |
calendar clock stopwatch metronome |
months hours seconds beats per bar* | |
| Energy | atmospheric electric temperature earthquake hearing atomic radiation |
pressure barometer electric meter thermometer seismograph audiometer Geiger-Müller tube |
millibars kilowatts degrees moment magnitude decibels, Hertz* particles per minute | |
| Space | length height of elevation capacity distance angle |
meter stick altimeter tape measure odometer protractor |
centimeters meters cubic feet miles degrees | |
| Matter | volume (capacity) mass (weight) density (liquid) |
flask scale hydrometer |
milliliters pounds specific gravity units | |
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When we want to measure something, there may be a standard unit (as above), more than one unit (e.g., meters or yards), or a unit and scale can be created. *The items indicated are actually ratios of measures. Scientists tend to focus on mass, length, and time and ways they combine. For example: speed = distance (length) / time (short periods) density = volume (three-dimensional space) / mass Vectors represent quantities with both magnitude and direction such as force, velocity, and acceleration. | ||||
Young children develop the concept that objects have various attributes, some of which can be measured. They develop the language to express measurement ideas such as longer or more. They begin to associate specific attributes with units and tools of measurement and make simple measurements fairly accurately. Elementary students gain experience with a variety of tools and measurement concepts, in both metric and customary systems. They work with formulas for perimeter, area, and volume of various shapes. By the secondary grades students gain experience with derived attributes (ratios of measurements), conversions, formulas, precision, and error concepts.
(http://www.teachervision.fen.com/math/pro-dev/55741.html?page=4&detoured=1)
Students with challenges learning mathematics, positive dispositions are a critical foundation for achievement. Teachers have the responsibility for creating classroom contexts that foster positive dispositions. Some concrete methods for promoting positive dispositions in students towards mathematics include:
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Seek out student interests and plan activities that make connections with those interests. For example, one entire class was interested in playing softball. They challenged other fourth-grade classrooms and kept statistics on every aspect of their games.
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Personalize math lessons by using student interests, names, real events, and student-created problems. Some teachers name classroom "discoveries" after students: "the Sally Brown proof."
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Allocate just two or three minutes at the beginning of each mathematics class to warm-up activities with familiar material. Begin with success!
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Create classroom procedures that allow students to take risks and make mistakes without punishment or humiliation.
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Encourage students to set personal goals in mathematics and keep track of their progress through individual portfolios or graphs.
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Check for student understanding when introducing new concepts and adjust explanations and examples until students demonstrate strong understanding. Check understanding by watching students work and by listening to their explanations, not through testing at this initial learning phase.
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Analyze students' mathematics knowledge and understanding for gaps that will hinder new learning. Plan remedial instruction that will fill those gaps by connecting concepts, not with isolated skills.
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Communicate clearly with students the "why" of mathematics for the year. What new learning will they accomplish? Why will it seem they are working on some of the same topics as last year? How will this learning be beneficial in the long run? Listen to students' explanations of their views of mathematics.
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When students have accomplishments, guide them in making explicit connections with their efforts.
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When students hit roadblocks, teach specific strategies for learning skills or procedures.
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Model positive dispositions-about mathematics and about working collaboratively with other teachers for student learning.
The combination of positive teacher and student dispositions towards mathematics learning will provide a critical component for success with mathematics instruction.
( http://www.teachervision.fen.com/math/learning-disabilities/55334.html#ixzz2WFAbYuLb
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