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Teaching and Learning Mathematics at the Middle Grades: Setting the Stage
Pages 19-38

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From page 21...
... THE MIDDLE SCHOOL LEARNER: CONTEXTS, CONCEPTS, AND THE TEACHING CONNECTION Thomas Dickinson, Professor of Curriculum and Instruction at Indiana State University.
From page 23...
... At the same time, a student's intellectual capacity to reason is expanding rapidly. Students in middle grades are growing in their ability to reason abstractly.
From page 24...
... MATHEMATICS OF THE MIDDLE GRADES As students encounter mathematics in the upper elementary gra(les, the emphasis changes from a focus on the additive structure of numbers and relationships to the multiplicative structure of numbers and relationships. This means that the students are faced with new kinds of numbers, fractions operations and decimals that rely on multiplication for their underlying structure.
From page 25...
... RATIONAL NUMBERS AND PROPORTIONAL REASONING One area of mathematics that is fundamental to the middle grades is rational numbers and proportional iThis strand argument is taken from a paper I presented at the Fourth International Mathematics Education Conference at the University of Chicago in August 1998 entitled Preparing Students for College and the Work Place: Can We Do Both?
From page 26...
... Study of mathematics involving quantitative reasoning invariably means reasoning about mathematics in contexts. Part of what makes mathematics so powerful is its science of abstraction from real contexts.
From page 27...
... GEOMETRIC SHAPES, LOCATION, AND SPATIAL VISUALIZATION Whether we are talking about an intending calculus student or an employee at a too} and die shop, geometry, location, and spatial visualization are important. Just as a calculus student nee(ls to visual MATH EMATI C S I N TH E Ml D DLE Size a curve moving to form the boundary or surface of a solid in space, a too} and die employee uses such skis to set a machine to locate and cut a huge piece of steel to specifications that truly exceed our imagination.
From page 28...
... ~ would argue that the study of chance or probability should be a part of the curriculum for all students in the middle grades. It is in these years that students have the interest and we can provide the time to experiment with random variables.
From page 29...
... Teach ing in the middle grades requires knowledge of the subject matter and also of students at this age. TEACHING MATHEMATICS IN THE MIDDLE GRADES What are the challenges associated with teaching mathematics in the
From page 30...
... Out of these student ideas come the conversations that, with the teacher's guidance, help make the underlying mathematical ideas, concepts, procedures, skills, and arguments more explicit for the students. As you think of the socialization of the middle school level, there is a natural match between the mathematical need to deeply understand ideas and the social need to inter act with ones peers around tasks that are of interest.
From page 31...
... SUMMARY While mathematics in the middle years is cognitively demanding, it is suited to the developing capabilities of MATH EMATI C S I N TH E Ml D DLE middle school students. New forms of classroom interaction, more emphasis on experimentation, on larger, more challenging problems, on seeking to understand and make sense of mathematics and mathematical situations, on using technology as a too} these are the ways in which new middle school curricula are seeking to engage these social, energetic, (leveloping a(lolescents in learning for their own future.
From page 32...
... " the voice asked and my grading reverie was broken. It was Amy Bounds, a seventh grader in my homeroom and a student in one of my social studies classes.
From page 33...
... Do you think ~ have enough? " And with that Amy extracted from her backpack a plastic bag stuffed with change anti ploppe(1 it on my (leek.
From page 34...
... That purpose was so that all of us would see development for what it is: a natural anti normal process, boun(le(1 by general psycho T E A C H ~ N G A N D ~ E A R N ~ N G MAT H E MAT ~ C S logical guidelines, but embodied in individuals. And this embodiment is bounded, shaped, and influenced by a range of contexts the individual context of self, that mixture of heredity and randomness; the context of family, street, neighborhood; the larger social context, which today includes an overwhelming and disturbing mass media context that impacts young adolescents at their every turn.
From page 35...
... Around the room there is a rich riot of color number lines, bought and teacher-made posters with vocabulary lists anti mathematics operations, and two computers (still not hooked up to the internet it's November when this is being written) in the back of the room by the teacher's desk.
From page 36...
... She thought she needed another challenge so she got licensed in mathematics and is in her secon(1 year of teaching that subject. Last year, her first teaching mathematics, 91% of her students passed the Texas Assessment of Academic Skills.
From page 37...
... At Me end of We class my notes summarize the lesson: · focus on reading directions · finding necessary information · using available data · drawing conclusions Tom data working in cooperative groups recording information accurately · doing basic mathematical operations . working alone · making choices to investigate individually ~ could tell you all the developmental psychology connections here, but ~ hope you see them.


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