Mathematics Education in the Middle Grades Teaching to Meet the Needs of Middle Grades Learners and to Maintain High Expectations: Proceedings of a National Convocation and Action Conferences (2000) / Chapter Skim
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Content and Learning Issues in the Middle Grades
Content and Learning Issues in the Middle Grades
Pages 39-60
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MATHEMATICS CONTENT AND LEARNING ISSUES IN MIDDLE GRADES MATHEMATICS Kathleen Hart, Chair of Mathematics Education (retired) , University of Nottingham, United Kingdom.
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There still remain enormously stubborn achievement gaps between white children and children of color; between poor children and financially advantaged children, between girls and boys. If asked the question, "How are we doing in the U.S.
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~ have often quoted Linda Reiff's comments to evoke an affirming chuckle from most middle grades educators or parents. She wrote: Working with teenagers is not easy.
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In sum, REFLECTIONS ON MIDDLE SCHOOL MATHEMATICS these young people are developmentally ripe for intellectual growth. But when they enter our middle schools every day, not many find in their classrooms a match for the intellectual intensity their questions renect.
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THE REFORM PICTURE While the middle school movement's thirty year history has secured a place on the reform map and has contributed CONTENT AND LEARNING ISSUES greatly to the overall improvement of many middle level schools, the movement's reform recommendations and efforts have, ~ believe been more successful in altering the climate and structure of mi(l(lle level schools than the curriculum and instruction our young people have experienced (FeIner, etal.,19971. Organizing smaller,more personalize(1 learning communities, commonly called teams, creating teacher scaffol(ling anti support for all students, emphasizing interdisciplinary planning anti teaching, anti creating more flexible sche(lules liberate(1 from tracking, have without question, raised teacher efficacy, encouraged professional (lialogue, re(luce(1 school anonymity, improve(1 school climate, anti even in some pockets, raised school achievement.
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While REFLECTIONS ON MIDDLE SCHOOL MATHEMATICS not always clear to the public nor consistently conveyed in professional development, we should not be too quick to blame the current achievement conundrum in mathematics or any field on the middle school concept. Interdisciplinary teaming, for in stance, remains at the core of middle school reform, in large part because of its research credibility to raise teacher sense of efficacy a key element in high performing classrooms.
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Fortunately, there are several themes that are recurring in current conversations among middle school advocates and those interested in mathematics reform which, when united, bring clarity and perspective to some of the more emotional attacks. Both groups call for a curriculum that is challenging and engaging for young people, offers connections across disciplines, challenges students to apply knowledge, putting mathematics to use, emphasizes problem-centered learning, provides opportunities for collaboration, and seeks to en(1 inequitable practices like tracking (Beane, 199Sb)
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As middle schools organize in small learning communities to ensure the noted benefits of teaming, students are grouped by mathematics levels in ways that can result in tracking and the reduction of mathematics learning for non-aIgebra students. These students deemed less ready or able, travel apart from algebra students, and may spend an entire year relearning mathematics concepts many already know, while they wait to enter "the algebra course." REFLECTIONS ON MIDDLE SCHOOL MATHEMATICS For young adolescents, meaning is everything.
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. Paper prepared for Middle Grades Mathematics Convocation, September, 24-25,1998.
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New Brunswick, NI: Transaction Books. REFLECTIONS ON MIDDLE SCHOOL MATHEMATICS Reiff, L
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In the secondary school, these subjects are allotted separate lime slots, anti the teacher only teaches that subject. The institutional life in school changes to a greater focus on formal learning, and in mathematics the concentration is on competencies and skills and their application.
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d. Alert the researchers to when the "formalisation" lesson or acceptance of MIDDLE GRADES MATHEMATICS the rule would take place and allow the lesson (s)
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Terence's Diagram for Equivalence CONTENT AND LEARNING ISSUES JOINING THE GROWN-UPS From the observations in CMF (an(1 some subsequent research) , it was plain that teachers and children embarked on a voyage of (liscovery to a place well known to the teacher.
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MIDDLE GRADES MATHEMATICS He had absorbed the "don't bother" but not when to use it. There were other instances in the interviews of children selecting a specific part of a teacher's statement and generalising incorrectly or of remembering the one erroneous statement the teacher had made.
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Do teachers redefine the operations to accommodate fractions and decimals? The middle grades is when children are trying to graft new concepts on hopelessly inadequate foundations put in place for counting numbers.
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Topic books; short "content" orientated material in four setsNumber, Space, Probability and Statistics, and Measurement; b) Core books; MIDDLE GRADES MATHEMATICS books of problems for an entire year to allow groups of mixed attainment to work together applying their mathematics; anti c)
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We were closely involved in all the trials and often marked the tests. In one school, the teacher agreed that the reason six children hall not reache(1 "mastery" level in the test was because they had not covered the entire book but only part of it.
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MIDDLE GRADES MATHEMATICS Hart, K (Eddy.
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Contrasting student solutions with adult solutions (Appendix 4J furthergrounds the conversation in a situation reading student responses that is in fact, part of the practice of teaching Marcy's Dots ~ ~_~ (Figure ~J from the 1992 National Assessment of Educational Progress grade test provoked a variety of responses rangingirom concern over the clarity of directions to surprise at the many and diverse ways students found their solutions. Common themes that emerged from the group discussions are described below.
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In some cases, there was concern over the lack of consistency between the work students did and their description of what they did. This was attributed to a lack of communication skills on the part of the students, although learning to communicate is an important middle grades topic.
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There was also strong agreement that content knowledge is not enough; teachers must learn how to help students bridge from the concrete to the abstract. ALGEBRA IN THE MIDDLE GRADES The issue of whether ad eighth graders are (levelopmentally really for aIgebra and how to position algebra in the learning environment of the child raised more questions.
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