Keywords: Number and Operation......
Ref: Krista16
Author(s): Bay-Williams, Jennifer; Martinie, Sherri
Date: 2003
Title: Thinking Rationally about Number and Operations in the Middle School
Journal or Publisher: Mathematics Teaching in the Middle School
Volume, Issue, Pages: Vol. 8, No. 6, 282-287
Reviewer: Krista
Date of Review: April 28, 2003
The Number and Operations standard from the Principles and Standards for School Mathematics states that students should be familiarity and understanding of rational numbers "should be developed through experience with many problems involving a range of topics." This article provided three example problems in which students would have to manipulate fractions and proportions in order to sovle. Each problem was centered around a situation that middle school students would be familiar with.
The first problem was about a group of students who were playing red light, green light. The problem listed the position of 12 students in fraction form from start to finish. For example, Bob was 8/9 of the way to the end. The students had to order from start to finish using mental math. This problem allowed students to use different methods and strategies figure out where to place the red light, green light students.
The second example problem posed involved a basketball coach who during a game had to pick a free-thrower after looking at her record book. The possible free-throwers had records of 17 of 25 free throws, 15 of 20 free throws, and 7 out of 10 free throws. Students who had to answer this problem were more accustomed to using decimals and felt uneasy about computing it otherwise. This emphasizes the need for students to become flexible using fractions, decimals, and percents.
The final example problem was about cutting 3 yards of ribbon into bows and each bow had to be 5/12 of a yard, how many bows could be made? This problem illustrated the need for students to be able to develop and analyze algorithms when computing rational numbers. After completing problems like these, students will begin to understand the standard algorithm for division by a fraction - multiplying by the reciprocal - that the denominator of the fractional divisor defines how many parts to split each whole and the numerator tells the group size, etc.
For students to be able to study and eventually understand ra tional numbers, problems need to be set in a context that relate to their world. The middle school focus should be centered on developing a students understanding of rational numbers, the reasoning behind it, and flexible use of numbers in a variety of contexts.
Keywords: Geometry, Measurement, Connections
Ref: Krista17
Author(s): Moore, Sara Delano; Bintz, William
Date: 2002
Title: Teaching Geometry and Measurement through Literature
Journal or Publisher: Mathematics Teaching in the Middle School
Volume, Issue, Pages: Vol. 8, No. 2, 78-83
Reviewer: Krista
Date of Review: April 28, 2003
Along with using a variety of manipulatives, teachers can use literature to teach mathematics. This article provided examples of how teachers can use literature to teach geometry and measurement and identified a variety of literary sources.
The article had two concept maps, which divided the literature that could be used to teach either shapes and measurements, or reasoning, topology, and dimensionality. Each concept map had 6 mathematical topics connected to 3 or more possible stories that related to that topic. For example, area and perimeter was a concept listed on the shapes and measurement map and "Spaghetti and Meatballs for All!" was a story listed. The story extends students' thingking about area and perimeter by describing how square units can be used to measure a shape's surface area and how to use units of length to determine the distance around tables of different shapes to seat dinner guests.
Using literature in the math classroom has many benefits. Many students might not be used to reading in a math class and this encourages a new type of thinking and reasoning. Along with providing many different types of literature that could be used in teaching many different concepts, the literature varied in difficulty, which would allow for differentiated instruction. While teaching about two-dimensional representations, the teacher could choose from "The Adventures of Penrose the Mathematical Cat," "Flat Stanley," or "Flatland" depending upon the students reading ability and ability to reason. Ultimately using literature to teach math creates new interest and conversations in the classroom.
Keywords: Activities, Connections...
Ref: Krista18
Author(s): Barger, Rita; Bryant, Cynthia
Date: 2003
Title: Calendar Capers
Journal or Publisher: Mathematics Teaching in the Middle School
Volume, Issue, Pages: Vol. 8, No. 6, 316-323
Reviewer: Krista
Date of Review: May 5, 2003
"Calendar Capers" was a 10-lesson unit for sixth grade students, which focused on using the calendar to teach math concepts such as mean, median, mode, range, fractions, finding and interpreting data. The unit had connections not only to everyday life, but to other disciplines as well and could easily be extended to become even more interdisciplinary.
The unit began by examining a January calendar, which listed the days in the format 1/365. From this calendar students were to infer and justify information such as what day of the week their birthday or holidays might fall on, how many Friday the 13ths there would be throughout the year, etc. This activity would allow students to discover patterns that occur like the occurrence of leap years in multiples of 400. Other activities during the unit involved gathering data on which day of the week the most babies were born, comparing the data of males and females, creating a graph to show the data, etc. The unit concluded with the creation of a calendar that featured holidays and celebrations chosen by the student. This activity would allow students to research holidays and historical events, and discover their significance.
This unit would probably be very interesting for students to participate in because it dealt with real world examples and let them be creative throughout, but it seemed to lack in teaching mathematical concepts. Most of the math concepts integrated into the unit would be ones that most sixth grade students would be familiar with, so it might be a tool to help students practice finding mean, mode, range, etc. To make this unit more worthwhile, teachers might use it as a supplement to another unit they might be teaching.
Keywords: Measurement, Activities...
Ref: Krista19
Author(s): Stern, Frances
Date: 2003
Title: How Many Students Tall is the School Building?
Journal or Publisher: Mathematics Teaching in the Middle School
Volume, Issue, Pages: Vol. 8, No. 5, 238-243
Reviewer: Krista
Date of Review: May 5, 2003
The question "how many students tall is the school building?" is taken from "How Big is the Moon? Whole Math in Action" which is geared towards fifth or sixth grade students. The purpose of this activity is to get the attention of the students while increasing their understanding of measurement, representative numbers, and the relationship between remainders and fractions.
The activity begins by posing the question of how many students tall is the school. Students then began to form questions of their own like they don't know how tall the school is, or the students are all of different heights. From these questions, students need to brainstorm solutions to the problem. Their solutions will draw on their previous understanding of mean, mode, and median. The activity can be left more broad to allow students to use a method they are most comfortable with.
The article suggests that this activity is best done in small groups. In their small groups, students can decide how to solve the problem, but they will be using their data collecting skills to find students' height and heights of the classroom, which would be used to find the heights of the floor and then the height of the building. Throughout this process students will be converting feet and inches and estimating fractions. This would also be an excellent time to introduce sample error when students find that their solutions might be different. Along with these skills, students will also be using estimation skills. Most likely they will find that their original estimate of the height of the building was much smaller than it actually was. The article included a rubric to score the students' work and ways to extend the project for others.
***********************
Keywords: Connections,
Ref: Krista13
Author(s): Koirala, Hari; Goodwin, Phillip
Date: 2002
Title: Middle-Level Students Learn Mathematics Using the U.S. Map
Journal or Publisher: Mathematics Teaching in the Middle School
Volume, Issue, Pages: Vol. 8, No. 2, 86-90
Reviewer: Krista
Date of Review: April 14, 2003
In order for students to build a mathematical understanding, they need to make meaningful connections to other disciplines. This article explained an integrated social studies and math lesson plan for fifth or sixth graders, where students used their understanding of the United States and a map to explore a variety of math concepts.
On the first day of the five-day unit students were given a worksheet that was divided into 5 columns. The first column listed 20 of the states. In the second column students were to estimate what the area of that state would be if the area of Connecticut was 1. After the students filled in column two, they were to discuss with a partner their personal estimates. In column three, they were to write their negotiated estimate, which could be an average of their estimates. During their discussion, students would have to explain their original estimate and find a method to determine the peer estimate. This activity was to take the entire class period and the students' worksheets were collected at the end of the period.
On day two of the unit, the worksheets were handed back to the students and they were also given an outline map of the United States. They were instructed to fill in column four, which was their estimate of the area of the states compared to Connecticut using the outline map. Students were not given a method for doing this so a variety was used such as: visually comparing, or creating a template of Connecticut to place in various states, etc. After they completed the worksheet, students were to reflect in a journal entry about their three estimates and which estimate was most accurate.
On day three of the unit students were given almanacs to find the actual areas of states. During this class period students discussed and defined ratio and scale.
Day four of the unit had students exploring the concepts of ratio, percentage, and mean by answering questions such as: Which are the biggest and smallest states in the United States, How many times larger is the biggest state compared to the smallest, What percent of the total land does it occupy, what is the mean area of all the states in New England. During this activity students were allowed to use calculators because the purpose was to do comparisons, not the computations.
On day five, the last day of the unit, student made graphs to show the data they had gathered on day four. Students were allowed to choose what graph they would like to use to represent their data.
Throughout the five-day unit students were using and learning multiple math concepts. Each mathematical concept had a real world application, so students could clearly see why certain skills were necessary through their applications.
Keywords: Teaching Strategies,
Ref: Krista14
Author(s): Allsopp, David; Lovin, Louann; Green, Gerald; Savage-Davis, Emma
Date: 2003
Title: Why Students with Special Needs Have Difficulty Learning Mathematics and What Teachers Can Do to Help
Journal or Publisher: Mathematics Teaching in the Middle School
Volume, Issue, Pages: Vol. 8, No. 6, 308-314
Reviewer: Krista
Date of Review: April 14, 2003
Some students with learning disabilities struggle to learn mathematics due to possessing learning characteristics that prevent them from learning math at the same pace as their peers. This article was divided into four categories: attention problems, cognitive-processing problems, memory problems, and metacognitive deficits. Each category was defined and issues with math problems identified. Teachers need to be aware of the variety of students in their classroom and develop instructional strategies that will result in instruction that moves from concrete, to representational, to abstract. Topics need to be taught in a meaningful context and their should be multiple opportunities to develop mathematical knowledge.
Students who have attention problems have heightened attention stimuli, which causes them to focus on everything. Therefore they are distracted from problem strategies and miss key steps in the process, which results in a gap in their knowledge base.
Students with cognitive-processing problems have disruptions in their central nervous system, which results in the alteration of messages received visually or auditorially and they copy information incorrectly. Teachers can help students by using more than one means of sensory input during instruction. A visual display could state a concept, students could receive a copy of the information, and the teacher could describe the information and have students summarize in their own words.
Memory problems cause students to have difficulty retrieving information quickly and accurately during problem solving. This can also cause difficulty when their are multi-step problems or equations. This can be addressed through mnemonic devices that students create so they can retrieve problem solving steps independently.
Students who have metacognitive deficits may not be able to identify and use strategies to complete tasks. For example when encountering a new problem they cannot apply past strategies. In these situations it would also b e effective to have students use mnemonic devices.
Students need to be empowered, so they can feel confident and successful in math. Students with learning disabilities are often encouraged to memorize information, which eliminates the making of meaningful connections. This further alienates students from understanding math. Teachers need to be prepared to explain and show concepts in multiple ways so all students can develop a deeper understanding of math.
Keywords: Algebra,
Ref: Krista12
Author(s): National Council for Teaching Mathematics
Date: 2001
Title: Navigating Through Algebra in Grades 6-8
Journal or Publisher: NCTM
Volume, Issue, Pages:
Reviewer: Krista
Date of Review: April 9, 2003
The purpose of this Navigation book is to guide middle school students through algebra by having them examine over arching themes of algebra such as: patterns, relations, and functions. While using this book students would learn to look at a mathematical situation, be able to interpret and analyze the information, and then represent their solution correctly using different methods. Students would become familiar using algebraic symbols, solving linear and nonlinear problems, and with representing information in graphs, tables, and equations.
The lessons outlined in this Navigation book all had real world applications that would have students engaged in hands-on problem solving. For example, one lesson I found especially interesting had students planning a fundraiser. They were given information and had to draw conclusions surrounding the amount of money raised and then they had to show their findings in tables and graphs. Throughout the lesson a variety of algebra skills were being used. Students were using algebraic symbols to represent data, they found slopes and intercepts, and used models to illustrate quantitative relationships. Not only were students learning and mastering these skills, but they could easily see the connection to their own life because schools host fundraisers quite often. This lesson could use actual numbers from the students' school and then they would actually be working on a problem that they could see direct results from.
Keywords: Geometry, Measurement, Manipulatives
Ref: Krista10
Author(s): Strutchens, Marilyn; Harris, Kimberly; Martin, Gary
Date: 2001
Title: Assessing Geometric and Measurement Understanding Manipulatives
Journal or Publisher: Mathematics Teaching in the Middle School
Volume, Issue, Pages: Vol. 6, No. 7, 402-405
Reviewer: Krista
Date of Review: April 2, 2003
According to the article many students struggle with understanding geometry. This is due to their lack of hands-on exploration of geometry, or their inability to view geometry in the real world. An experiment was conducted to prove this, and ideas were provided to help students make connections in geometry so they could reach a higher level of understanding.
The experiment conducted consisted of asking groups of fourth, eighth, and twelfth grade students three questions that dealt with geometry and measurement. The questions all related to three given shapes, a square and two triangles. Students were asked to explain which shape was different than the other two, which shape had the longest perimeter, and which shape had the largest area. Most students were able to answer which shape was different and their responses of why varied in level. Some eighth graders were able to differentiate by describing properties of the shapes while others were at the first level of thinking and were only able to explain visually. For the following two questions, the majority of students were not able to answer correctly. Some were able to identify the shape with the longest perimeter, but could not explain why. The area question also was not answered correctly by the majority of students. The results of the test showed that students could complete uncomplicated tasks, but could not justify their answers in comparing complex figures. This means that students need more experience with a variety of geometric figures in a more complex setting, so then they will be able to develop an ability to visualize figures and their properties.
The article states that teachers need to create activities, which will allow students to sort shapes due to their geometric attributes, identify shapes according to properties, and determine the fewest properties needed to describe a shape. These activates involve the discovering the relationships among shapes. One example to help with area was to use show the relationship between
en a parallelogram and a rectangle. Students could see this by creating family trees that show relationships. Ultimately students need a more meaningful understanding of geometric figures, instead of simply memorizing properties, so they can form connections.
Keywords: Technology, Teaching Strategies,
Ref: Krista11
Author(s): Thompson, Anthony; Sproule, Stephen
Date: 2000
Title: Deciding When to Use Calculators
Journal or Publisher: Mathematics Teaching in the Middle School
Volume, Issue, Pages: Vol. 6, No. 2, 126-29
Reviewer: Krista
Date of Review: April 2, 2002
The National Council of Teachers of Mathematics encourage the use of calculators in middle school classrooms because they allow worthwhile discoveries in math. Many teachers struggle with determining when to use calculators, so this article provides a framework to help decide when calculator use is appropriate.
The basis of the framework for deciding whether students will use calculators consists of first focusing on the needs and abilities of the students, and then examine the teacher's motives and goals in a mathematical activity. This examination allows for teachers to put students first and decide if a calculator is essential or nonessential during an activity. A calculator is essential in the process if the activity would be too complex without the use of it, and the goal of the activity is not a computational answer. A calculator is nonessential if the product of the activity is a computational solution. These two reasons are separate because they have two different goals, finding computational solutions and engaging in problem solving strategies.
By creating a framework, teachers can change the way they use calculators in their classroom and focus on whether it is essential and help in analyzing real world data, or nonessential if their goal is a process.
Keywords: Measurement
Ref: Krista9
Author(s): Geddes, Dorothy
Date: 1993
Title: Measurement in the Middle Grades - Addenda Series
Journal or Publisher: National Council of Teachers of Mathematics
Volume, Issue, Pages:
Reviewer: Krista
Date of Review: March 12, 2003
The statement "measurement is an intrinsic part of our everyday living" begins the introduction of this book. This is the core concept that all lessons and ideas in the book support. Measurement is a part of everyday life, and practice using it instills the importance of having mathematical skills. Since measurement is so applicable to life, the examples used should reflect real world applications. This book provides both lesson and example ideas that stress estimating, measuring, discovering patterns and connections, and interdisciplinary projects.
The sample activities focus on students investigating and discovering formulas and applying them to real world situations. If students are given these sorts of examples they will not only be expanding their mathematical understanding, but developing thinking skills.
One example I especially liked from this book used the movie "Honey I Shrunk the Kids" to illustrate proportions. By bringing a movie into a math class, something out of the ordinary, I think students will be intrigued as they try to figure out the problem. There were multiple examples like this in the book and interdisciplinary projects, too.
Keywords: Algebra, Connections,
Ref: Krista8
Author(s): Chappell, Michaele; Strutchens, Marilyn
Date: 2001
Title: Creating Connections: Promoting Algebraic Thinking with Concrete Models
Journal or Publisher: Mathematics Teaching in the Middle School
Volume, Issue, Pages: Vol. 7, No. 1, 20-25
Reviewer: Krista
Date of Review: March 10, 2003
When students are not exposed to ideas and connections in mathematical teaching, they are unable to learn skills and concepts effectively. Students view algebra as symbol manipulation instead of "a way of thinking, a method of seeing and expressing relationships," which inhibits them from making the necessary connections. This article explains how an algebra lesson can use concrete models to teach the notion of variable, number properties, and geometry.
Students can use algebraic tiles to represent variables, an idea that can be vague to some students. By assigning tiles their own variables, students can understand that the letter is arbitrary, so they will not become fixated on using x and y.
Students can use tiles to demonstrate number properties by modelling x+5 and x+y. By manipulating the individual rectangles that represent x and y to form the product, students can show the answer in different ways while seeing the commutative property. The zero principle, as well as the distributive property can also be done using tiles.
Geometry and algebra can be connected in an activity that relates the product rectangle (created during the binomial example) and area. For example, a rectangle that is (y+5) by (y+3) forms a product rectangle with an area of y2+8y+15.
Using concrete models teaches concepts in a different way and addresses the different learning styles of students in a classroom. By showing an algebraic concept with the tiles, students can form connections, which will help them understand past, present and future math concepts.
Keywords: Problem Solving
Ref: Krista7
Author(s): Billings, Esther M
Date: 2001
Title: Problems That Encourage Proportion Sense
Journal or Publisher: Mathematics Teaching in the Middle School
Volume, Issue, Pages: Vol. 7, No. 1, 10-14
Reviewer: Krista
Date of Review: March 4, 2003
When completing math problems, students get caught up in using formulas and computing the numbers instead of understanding the question and reasoning. This article focused on this problem when students solve proportion problems. At times students immediately plug numbers into a formula and reach an incorrect answer, but do not realize that it does not logically make sense. Instead of applying numbers to formulas students should concentrate on the relationships between proportions.
By removing numbers from proportion problems, students can study the relationship and use proportion sense to come to a reasonable conclusion. This also allows the problem to be open ended and students can analyze more possibilities for an answer without being overly concerned with finding a numerical answer.
If used properly, numeric problems can also develop proportion sense. By first doing and discussing nonnumeric problems students will have an understanding of proportions, then those same problems can be done using numbers. Students will have taken the proportion sense they learned and applied it to a concrete numeric problem. Before immediately going to solving the problem, students should be encouraged to ask a few logical questions about the problem, so when they find an answer they will be able to see if it is actually possible and if their strategy for solving it is accurate.
Proportions are very applicable to real world problems, but if only numeric computations are the focus students will not gain the reasoning that will help them solve these problems. The relationship between proportions should be the focus, which will ultimately help students retain the knowledge.
Keywords: Standards
Ref: Krista6
Author(s): Stein, Mary Kay
Date: 2001
Title: Mathematical Argumentation: Putting Umph in Classroom Discussions
Journal or Publisher: Mathematics Teaching in the Middle School
Volume, Issue, Pages: Vol. 7, No. 2, 110-112
Reviewer: Krista
Date of Review: March 4, 2003
The NCTM standards recommend that students should be responsible for thinking and reasoning. Classroom discussions, instead of listening to a lecture, allow students to construct and evaluate what they are learning. It seems like a difficult task to have a discussion in a math class without just having a teacher ask a student to explain how to solve a problem, but it can be done and this article provided several tips.
By providing the students with a problem and asking them to solve it, you might see several different types of methods. Having students share their method with the class encourages students to listen to one another, try to understand different methods, and critique other approaches. When solutions are incorrect students can discover why a method did not work, providing a more in-depth understanding.
For students to be able to participate in a mathematical discussion, the teacher needs to create a classroom atmosphere where students feel comfortable sharing and that even wrong answers help the learning process. Students also need to be comfortable using math terminology for a discussion to take place. The more practice students have in discussing math, the more they are learning on their own.
Keywords: Teaching Strategies, Algebra,
Ref: Krista3
Author(s): Lewkowicz, Margie
Date: 2003
Title: The Use of "Intrigue" to Enhance Mathematical Thinking and
Motivation in Beginning Algebra
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: Vol. 6, No. 2, 92-95
Reviewer: Krista
Date of Review: February 19, 2003
On the first day of class of Math Education, Professor Wallace told the class that she expected her students to memorize the textbook since she did. We could test her ability by picking a 3 digit number, subtracting it by the reverse of the number and dividing that in half. From our result, Professor Wallace could name the last word on that page number. The technique she was using was referred to in "The Use of "Intrigue" to Enhance Mathematical Thinking and Motivation in Beginning Algebra."
The intrigue model consists of think of a number problems that appeal to students because they wonder how the answers to the problems are possible. Using Professor Wallace's example, we knew she had not actually memorized the 400 hundred pages of our textbook, but how she was able to know what our results would be tempted us to find out how it was all possible. The journal article provided three other intrigue model problems that were suitable for beginning algebra.
As students attempt to solve these problems or find the pattern they plug in many different numbers. Simply trying numbers will not prove why the "trick" works, but by using algebraic operations it can be proved. Students are no longer overwhelmed with the memorization of formulas, but instead they are stimulated by trying to find the pattern, which requires proving it and therefore using algebra skills such as combining like terms, the distributive property, and place value.
Like
there name, intrigue problems get students' attention and encourage them to look at math from
another angle. While either working on them individually, or as a class, students feel a sense of
accomplishment when they solve these problems.
Keywords: Teaching Strategies, Connections,
Ref: Krista4
Author(s): Olson, Joy Clay
Date: 2003
Title: Interdisciplinary Projects Enhance Teaching and Learning
Journal or Publisher: Mathematics Teaching in the Middle School
Volume, Issue, Pages: Vol. 8, No. 8, 260-266
Reviewer: Krista
Date of Review: February 20, 2002
Through completing interdisciplinary projects, students are able to make connections between subject areas, which encourages retention of information for longer periods of time because they are using the skills in different settings. For many students a lot of mathematical principles seem very isolated from the real world and many time they do not see how equations actually apply to anything else, but the projects and activities listed in this article provided examples of how this stigma can be eliminated.
The main project the author described in the article occurred between social studies, science, language arts, and her math class. Students were to create a country and civilization. Math was incorporated into the project as students had to create scale outlines of their country as well as explore how perimeter and area affect shape. Percentages had to be used in determining how much of their country was covered with certain types of land. This project provided students an opportunity to use certain math skills, but also a real world example to apply it to. Students were also using their math skills in other classrooms, which gave them more practice and teachers found that the students remembered things more often.
Besides creating a country students of the author also chose a problem that affected their community. Examples included school bus crowding, littering, school crossings, and exhibitions of racist behavior. After identifying a problem, students gathered and analyzed data. From their data they actually made recommendations to the proper people on how this problem could be remedied. The students' now had a practical purpose for their work and it was meaningful to them because they did both the research and brainstormed solutions.
Obviously math was used throughout their work as they gathered and processed data, but
it was also used in the presentation aspect through graphs. Students also became comfortable
using mathematical terminology as they explained their projects to others. In doing such a
project students were able to develop skills they will use throughout life and see how math is
used in different fields of work.
Keywords: Algebra, Teaching Strategies,
Ref: Krista5
Author(s): Gratzer, William
Date: 2003
Title: Maps and Algebra
Journal or Publisher: Mathematics Teaching in the Middle School
Volume, Issue, Pages: Vol. 8, No. 6, 300-302
Reviewer: Krista
Date of Review: February 24, 2003
By taking a situation that is relevant to a student's life and applying it to mathematics, students are more likely to remember it and develop a greater mathematical understanding. "Maps and Algebra" gave an example of such a technique. By comparing the reversal of map directions to linear equations, students can become familiar with how to reverse the operations to solve a linear equation.
This technique can be used by giving students a set of directions. For example, have students draw a map of the following directions: Robert walked 3 blocks north, then 8 blocks east, then 10 blocks south, and then 2 blocks west. Then tell students Robert needs to go back. Students will see that Robert both reversed direction, but also the original order. By creating a table with two columns, which shows each stop step-by-step with the 2 paths next to each other, this can be even clearer to students. This relates to a linear equation because it can be looked at like a set of directions. For example, 8=3x+2 is the directions of an input x, multiplied by 3, then added 2 to equal 8. To solve this linear equation you work in reverse. Start with output 8, subtract 2, divide by 3, end with input x=2. This step-by-step process can be made clear by making another table with the 2 "paths" next to each other, but also with a third column showing the computations.
By practicing this method, students will become familiar with the steps involved in solving linear equations. It will also be memorable because it relates to real life. The creation of a table also is a visual tool, which ensures that students take each equation and solve it step-by-step.
Keywords: Connections
Ref: Krista1
Author(s): Bartels, Bobbye Hoffman
Date: 1995
Title: Promoting Mathematics Connections with Concept Mapping
Journal or Publisher: Mathematics Teaching in the Middle School
Volume, Issue, Pages: Vol. 1, No. 7, 542-549
Reviewer: Krista
Date of Review: February 18, 2003
Concept mapping is a tool for students to use to visually make mathematical connections among key ideas. A concept map can consist of bubbles with arrows connecting concepts from a lesson. The arrows are labelled with linking words, which specify the relationship between the concepts. The most general mathematical idea is placed at the top of the concept map and as the concepts get more specific they are placed below the first idea and the so on. Along with telling what the connection between ideas is, students could also provide an example that relates to the real world.
Concept mapping can be used at multiple levels of mathematics. It can be used to visually explain the relationship between quadrilaterals and also used to describe linear equations. Concept maps could range from simple to more complex, but all would provide a visual representation of mathematical connections.
Throughout an instructional unit concept mapping could be used. Each day as students gain more information during a lesson from the unit, they could add that knowledge to a concept map. At the end of the unit, students would have a complete concept map of all they had learned and how each topic connects to one another. In following units of the class, students could link entire concept maps to previous ones creating a mathematical big picture.
Concept mapping can be done in a variety of settings: individual, small group, or as an entire class. Each type of group allows for different types of learning to take place. As an entire class a concept map could be completed with the aid of the teacher. As a small group students could work together to complete a concept map, which encourages communication and mathematical reasoning. When students work individually they are able to see if they picked up on the main idea.
Not only are concept maps helpful for students, teachers can also use them to assess what the student has learned. By providing students with a blank concept map and a list of key ideas or principles from a unit, students can fill the map in and appropriately explain the connection between ideas. Through this type of assessment teachers would be able to see if students understood the key concepts as well as how they were interrelated.
When teachers emphasize connections while teaching, mathematics becomes interrelated and linked to real world applications. Therefore students not only learn individual ideas and concepts, but are also able to see the larger mathematical picture.
Concept
mapping would be a very valuable tool in a classroom. In a students' mind lessons would no
longer be separate equations, terminology, and concepts, but connected ideas, which they would
be able to explain with words and visually see how it all relates.
Keywords: Assessment
Ref: Krista2
Author(s): Williams, Nancy & Wynne, Brian
Date: 2000
Title: Journal Writing in the Mathematics Classroom
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: Vol. 93, Num. 2, 132-135
Reviewer: Krista
Date of Review: February 18, 2003
According to the NCTM, "The assessment of students' ability to communicate mathematics should provide evidence that they can express mathematical ideas by speaking, writing, and demonstrating and depicting them visually." In high school, my experiences with mathematics ultimately did not allow me to do this, instead I was evaluated at the end of a unit by a test that consisted of the application of equations that had been learned. It is important to learn what I did, and be able to apply it, but it limited me from gaining a greater understanding of mathematics. Journal writing allows students to approach mathematics in a different way and use a variety of thinking skills.
The article described an experiment of journal writing in a math classroom. Through their experiment they gave tips on how to effectively use journaling and what to avoid. For example, by assigning a topic for students to write about that had been discussed that day or earlier and providing time in class, say ten minutes, to do their journals on a regular basis journal writing become a natural part of the math curriculum. It should not be used as filler work, but instead a way for students to give feedback on understanding of a lesson and a way to gauge their own understanding. It also gives students an opportunity to use mathematical vocabulary and become comfortable with it. As the semester progresses and ideas become more complex, students can look back at their previous entries and see what they have learned and how it relates.
The article said that many students were reluctant to write in journals because "you don't write in math class." As students became more at ease with writing mathematically, they began to more readily express their thoughts on math concepts.
Teachers can use the journals to assess student understanding, as well as their approach to mathematical reasoning. By carefully choosing journal topics, teachers can guide students in making the connections between concepts and see that they are finding them. This gives a greater idea of why a student either struggles or excels in certain areas.