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Sherri L. Martinie

Teachers who are skilled at recognizing students' misconceptions about decimals are better equipped to make instructional decisions that build on these ideas.

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Sherri Martinie

The role of understanding in learning mathematics has been referred to in textbooks from the 1800s and has been supported throughout the 1900s by psychologists, philosophers, and educators. Despite its persistent appearance, the importance of understanding continues to be questioned for several reasons. First, many adults view school mathematics as something separate from the mathematics needed in everyday life. The mathematics they learned in school was dominated by isolated facts, skills, rules, and procedures to be memorized and practiced. It has been reported that the mathematics curriculum is shallow, undemanding, and covers too many topics superficially (Kilpatrick, Swafford, and Findell 2001).

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Sherri Martinie

Students are more motivated to learn mathematics when they recognize that it has value. Collecting and analyzing data that is meaningful and interesting to students can emphasize valuable mathematics.

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Sherri Martinie

The purpose of the “Families Ask” department is to help classroom teachers respond to questions commonly asked by caregivers of their students. A commonly asked question will be posed; a rationale for the response will be presented for teachers; and a reproducible page will be offered for duplication and distribution to parents, other caregivers, administrators, or community members—anyone involved in the mathematical education of middle school children.

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Sherri Martinie

Children who claim not to like mathematics are often the same ones who demonstrate little persistence and motivation. They are sometimes unwilling to try new problems and will often respond to questions with an “I don't know.” Even one student who professes not to like mathematics is too many. Sometimes this attitude can be contagious. The feeling of inadequacy that accompanies this attitude can lead to disruptive behavior that interferes with the learning of all students. Something must be done to improve this attitude, but what?

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Sherri Martinie and Janet Stramel

Students of all ages need to do math to understand math. Manipulatives provide a way for students to do mathematics in a concrete manner, and they learn some mathematics concepts better when explored with manipulatives. Middle school teachers sometimes fail to see the purpose of manipulatives, citing reasons such as time constraints and management problems, and generally feel that they are not important. Training students in the appropriate use of manipulatives alleviates many management problems and results in the effective use of time. Learning new concepts in the middle grades is just as complex a task as learning new concepts at grades K–3.

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Sherri Martinie

The value of building a strong understanding of measurement must not be underestimated. The skills of measurement are frequently encountered in realworld situations, from measuring the size of a room to measuring the time it takes to run a mile in gym class to the amount of water used when a faucet drips. Instruction involving measurement should focus on teaching students, K–12, to 'understand measurable attributes of objects … and apply appropriate techniques, tools, and formulas to determine measurements' (NCTM's Principles and Standards for School Mathematics, p. 44). These measurements may be one, two, or three dimensional and involve length, weight, capacity, time, or temperature. However, research on measurement reports that this concept harbors the largest discrepancy between learning opportunities and actual performance, meaning that although students are instructed in measurement skills in school, they cannot show that they have learned the concept.

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Jennifer M. Bay-Williams and Sherri L. Martinie

Six thought-provoking issues challenge misconceptions about this iconic topic.

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Jennifer Bay-Williams and Sherri Martinie

A lgebraic thinking is a critical skill for all students. Algebra is the study of patterns, and patterns span the curriculum. Algebraic thinking can support students' learning of many topics. For example, if students collect data on the radius, diameter, and circumference of various-sized circles and look for patterns in their data, they will discover the formula for the circumference of a circle. Similarly, if students explore patterns in problems like 3 ÷ 1/2 (how many 1/2s are in 3?), 4 ÷ 1/4, and 2 ÷ 1/5, they will begin to develop a strategy for the division of fractions (multiply by the denominator). Algebraic equations are used to describe real-world phenomena and can then be used to predict new phenomena. For example, if you know that you can walk 3 miles in an hour, then you can determine a distance for any amount of time (d = 3t), or how much time it will take to cover any distance (t = d/3).

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Edited by Sherri Martinie and Grace Dávila Coates

The importance of number sense and research documenting students' struggles with number sense has gained prominence in the past twenty or more years (Post 1981; Reys, Kim, and Bay 1999). Students who have number sense have a better feel for numbers, their meanings and representations, and operations than those lacking this skill. They are also more confident when working with numbers. In addition, they are flexible in their thinking and will often invent their own computational procedures and problem-solving strategies. They are able to judge the reasonableness of solutions and adjust estimates when necessary.