Keywords: Proof, Keyword 2, Optional..., Keyword 3, Optional...
Ref: Becca21
Author(s): Sconyers, James
Date: December, 1995
Title: Proof and the Middle School Mathematics Student
Journal or Publisher: Mathematics Teaching in the Middle School
Volume, Issue, Pages: 1(7), 516-518
Reviewer: Becca
Date of Review: 5/5/03
Why is it that many students feel uncomfortable with doing proofs? One reason may be because many times proof is left out of any work in math until high school. Students become overwhelmed with it because it is so unfamiliar to them. Part of the problem may also be a teacher’s understanding of what a proof is made up of. Many times, the missing link that is preventing middle school students from learning and understanding proofs is concrete exploration. James Sconyers gives an example. “Begin with a convex polygon with a given number of sides. Connect two points with a segment. How many sides do the two resulting polygons have altogether?” Students explored this by drawing out many convex polygons and tried to find a pattern. They concluded that the new polygons have 2, 3 or 4 more sides than the original. A counterexample could not be found. The conclusion that students came to did not prove anything, but they now have the experiential bases to make the connections to formulate one.
Proof doesn’t need to be difficult. It can be helpful for students to make the transition from concrete to abstract. Once students are introduced to proofs at a middle school level, they will be more prepared and a lot more comfortable with it once they reach high school.
When I read this article, I immediately thought of myself. Proofs are one aspect of math that I really don’t enjoy. I have always struggled with the concept and reading this article made me feel like I wasn’t alone! I think proofs definitely do need to be taught beginning in middle school so students don’t feel so overwhelmed. If I would have been introduced to proofs earlier, I may have more positive feelings toward the concept.
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Keywords: Connections, Teaching Strategies, Curriculum
Ref: Becca19
Author(s):
Date: December, 2001
Title: Mrs. Whatsit "Socks" It to Probability
Journal or Publisher: Teaching Children Mathematics
Volume, Issue, Pages: 8(4), p. 246-249
Reviewer: Becca
Date of Review: 4/28/03
This article talks about how both the ideas of writing across the curriculum and connections in math can be integrated into one classroom. Children’s literature offers a wealth of opportunities for teachers to help students make connections. Many books contain isolated scenes that can be used as springboards to math topics.
For example, during A Wrinkle in Time, Mrs. Whatsit takes off her boots and has a red and white striped sock and an argyle sock on. This can lead to the question, how many individual socks must be drawn from a drawer to guarantee that you have a matched pair? This then led into a class discussion, which clarified the difference between activities involving replacement and nonreplacement of drawn items, and explained concepts of population and sample space. Other concepts of probability can be explored by introducing an attribute set based on Mrs. Whatsit’s socks. Students explored the sets and determined how the socks are alike or different. Basically this situations of “socks in the drawer” can be used to investigate probability, either theoretically or empirically.
Curriculum integration helps students see the meaning of the concepts they’re learning and how this learning relates to their immediate and future interests and needs. I believe that using literature in a math classroom is a great way to integrate curriculum. It is also a great way of getting students to do math in a more round about way then most are probably used to. I think it’s something I definitely would like to try in my classroom someday!
Keywords: Issues, , Keyword 3, Optional...
Ref: Becca20
Author(s): Levi, Linda
Date: December, 2000
Title: Gender Equity in Math Education
Journal or Publisher: Teaching Children Mathematics
Volume, Issue, Pages: 7(2), p. 101-105
Reviewer: Becca
Date of Review: 4/230/03
Gender equity in math is a complex subject. Although guys and girls take similar classes and achieve similar scores on standardized tests, male’s participation in math after high school is far greater than female’s. Linda Levi decided to interview some elementary school teachers to see how they address the problem of gender equity in math education. There were three overall roles these teachers play in confronting the issue. The first is to provide equal opportunities and respect differences. The teachers try to ensure that they give male and females the same types of opportunities to learn math and participate in math activities. The second role is to ensure that girls and boys have the same experiences. This includes treating them equally, calling on boys and girls the same amount, and even making sure there is an equal amount of male and female names in story problems. The third role is to attempt to compensate for gender differences in society. Teachers said they made conscious effort to promote girls’ interest in math and related activities. Some even take the time to discuss gender stereotypes and that gender does not need to influence a person’s interests or career options.
No teacher was completely consistent in adopting any one of the three roles. After examining teacher’s beliefs, Levi is more convinced than ever that we need to use our best problem solving strategies to work toward gender equity. We must define the problem, reflect on decisions we make and examine the influence of these decisions on the children in our classes.
I thought this was an extremely interesting article because I think that there are definite gender differences within school, so to read about them specifically as they relate to math really provided me with some good information. I always thought that males excelled quite a bit more in math than females, but according to this, their scores are fairly equal. I think being aware of gender differences within a math classroom is very important and reading about what other teachers had to say about it will be helpful when I teach someday.
Keywords: Assessment, Geometry
Ref: Becca18
Author(s): Erich, David
Date: September, 2002
Title: Authentic Assessment in the Geometry Classroom: Calculating the Classroom Air-Exchange Rate
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: 95(6) p. 422-424
Reviewer: Becca
Date of Review: 4/23/03
The idea for this project originated with a question from a geometry student while she observed technicians measuring and balancing the fresh air-flow into a teacher’s classroom. The class happened to be in the middle of a unit on volume and the teacher couldn’t pass up an opportunity to apply volume calculations to it. The teacher had the technicians explain what they were doing and he actually used some of the same terms the teacher was using during this particular unit.
The teacher used the room air-exchange activity sheets at the end of their unit on volume to assess students’ understanding of the concept. The teacher felt it was a good and important assessment tool because it required students to apply equations and techniques that they had learned to a context of their physical world. It required measuring the students’ physical surroundings, calculating area, volume and flow rates on the bases of those measurements, researching state and local building codes and converting units to compare those results. Students also presented findings orally and in writing. The teacher stated, “this room air-exchange project is an assessment that gives me the ability to assess whether a students truly understands the concepts of area and volume and how those concepts are applied to real life situations.”
I thought this was quite an interesting article because I never would have thought to use such a project as a form of assessment. I think it’s a great way to combine real life situations to math while also making it relevant to the particular topic being discussed.
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Keywords: Number and Operation,
Ref: Becca16
Author(s): Moldavan, Carla
Date: December, 2001
Title: Enriching Numeration and Number Operations
Journal or Publisher: Teaching Children Mathematics
Volume, Issue, Pages: 8 (4), p. 238-243
Reviewer: Becca
Date of Review: 4/13/03
The first thing students hear when they walk in the classroom is, “Pretend that you live on an island and have no contact with others. You don’t know words or written symbols for numbers. Your task is to develop a numeration system – a method that would allow you to count coconuts or shells.” This task was the first one given to fourth graders in an attempt to integrate multiculturalism in their curriculum. This introduction led into work with numeration systems and algorithms from other cultures.
First students looked at the written symbols of the Egyptian numeration system. This introduced students to Egyptian numerals and added meaning to our own decimal system. Students changed decimal-system numerals to Egyptian numerals and also moved on to adding and subtracting them. This helped students explore the meaning of regrouping. After that, students were given base-ten blocks and were asked to illustrate sample problems. Students understood this algorithm produced the same result and is an acceptable way of subtracting. A few more different types of methods were used, including the lattice method for multiplication (developed in India), doubling (an Egyptian method) and the duplation-and-mediation method (Russian-peasant algorithm). While students were practicing multiplication, they gained a multicultural perspective as well.
This was a great way of integrating culture into the classroom and making students realize how many different ways there are of doing math. I thought the way the teacher introduced this was especially interesting just because I think students are a lot more likely to be interested than if they just started the unit.
Keywords: Communications,
Ref: Becca17
Author(s): Buschman, Larry
Date: December, 2001
Title: Using Student Interviews to Guide Classroom Instruction: An Action Research Project
Journal or Publisher: Teaching Children Mathematics
Volume, Issue, Pages: 8(4), p. 222-227
Reviewer: Becca
Date of Review: 4/15/03
The purpose of this research project was to investigate how student interviews would influence the way teachers present math in the classroom. Teachers were struggling to implement problem solving into their math classrooms. They realized they lacked sufficient knowledge about the mathematical understanding of individual students. The goal was to answer the two following questions: 1. Do student interviews provide teachers with more detailed, accurate and complete pictures of children’s math understanding? 2. Does this knowledge help teachers improve the way they teach math?
It was found that the student interviews directly supported two of the approaches to teaching math that are used at Jefferson Elementary (the place where this project took place). Understanding is personally constructed and the interviews helped teachers to understand how different children learn math in different ways. In regards to the second question, student interviews changed instructional practices in some classrooms and influenced instruction in all classrooms. All teachers reported that they increased their focus on meeting the needs of individual students. Some teachers were able to identify students who were ready for the next level of conceptual understanding, some were able to write better problems for use in the classroom and some tried to make the classroom more conducive to discussing children’s solutions to problems. Overall this seemed to be a very positive experience for both teachers and students. Teachers were able to gain a more accurate and complete view of what children know and can do and children were able to benefit directly from the interview process by spending one on one time with the teacher – a rare valued opportunity.
I thought this was a great research project that obviously turned out to be very beneficial for everyone involved. I definitely think there is value in student’s opinion in what they learn and how they learn it. If you’re teaching in a way that isn’t reaching students, then you should know that and be willing to change. Conducting interviews is obviously a very time consuming thing to do, but I feel that in some cases could be necessary. This was definitely an interesting article to read and makes me realize how important students are in their own learning.
Keywords: Measurement,
Ref: Becca15
Author(s): Young, Sharon L. & O'Leary, Robbin
Date: March, 2002
Title: Creating Numerical Scales for Measuring Tools
Journal or Publisher: Teaching Children Mathematics
Volume, Issue, Pages: 8(7), p. 400-405
Reviewer: Becca
Date of Review: 4/9/03
It is important to involve students in activities that would encourage them to think mathematically about the need for creating measuring tools with numerical scales. Many ideas must be addressed before students can understand measuring scales on rulers, measuring cups and thermometers so first grade students in two schools participated in activities that addressed these ideas.
During the first main activity, the story “How Big is a Foot?” was used to get students and then they had to work in groups to explore what happens when different sized units are used to measure the same object. Their task, what happen when we measure something with long footprints, then with short footprints? During the second lesson, students discussed difficulties they encountered while measuring with the different sized footprints. The third activity focused on transferring the knowledge gained using non-standard units and rulers using standard units of an inch and a foot.
The second main activity focused on measuring the quantity of water or rice that a large container would hold when small drinking cups were used as a unit of measure. Students had difficulty with this task because they couldn’t visualize how individual cupfuls would appear inside the container.
Throughout the activities, students were encouraged to think like mathematicians. In the process of developing numerical scales, they learned that the size of a unit affects the numerical values in a predictable fashion and must be selected in relation to the size and type of the object being measured. The theory that students should measure lengths using individual non-standard units before they begin working with non-standard rulers and numerical scales is a very interesting one to me. I think it’s actually a really good idea and one that enables students to understand the concepts of measurement a lot better.
Keywords: Algebra, Standards,
Ref: Becca14
Author(s): Bay-Williams, Jennifer M.
Date: December, 2001
Title: What is Algebra in Elementary School?
Journal or Publisher: Teaching Children Mathematics
Volume, Issue, Pages: 8(4), p. 196-200
Reviewer: Becca
Date of Review: 4/7/03
Principles and Standards identify four major themes for the algebra standard for K-12: 1. Understand patterns, relations and functions 2. Represent and analyze situations 3. Use math models to represent and understand quantitative relationships 4. Analyze change in various contexts The skill that begins in kindergarten as recognizing and extending patterns develops over the course of elementary school to generalizing problems verbally and symbolically in fifth grade. This article discusses three classroom explorations that help illustrate how these expectations are met in practice.
The first activity, called Card Patterns, is a simple game where cards are placed in a row and one card is turned over at a time. Students are to look for a pattern and predict the next card. The algebra content here is found in the students’ describing and extending numeric patterns. The second activity, called Pattern Block Patterning, is where students studied patterns to predict the number of pattern blocks it would need to build the 20th and 30th designs. It required students to extend a geometric pattern, generalize it and represent it geometrically. It also gave many students an opportunity to write the algebraic expression for the pattern in symbols. The third activity, called Creating and Analyzing Color-Tile Patterns, is where students create their own designs with color tiles, record the data in tables and graphs, and use that information to determine the general rules for their designs.
Algebra builds on students’ experiences with numbers. In each example, students used their knowledge of skip counting and whole number operations to look for patterns. Educators must provide algebraic experiences that are developmentally appropriate and grow in sophistication for students in grade preK-5. Algebraic experiences in elementary school are essential in building the thinking that it is an important precursor to the study of algebra in middle and secondary schools.
This article was extremely informative for me and I would definitely recommend reading it. When I think of algebra, I don’t connect it to the elementary level very well. Reading about various activities involving algebra that can be implemented at the elementary level made me realize that algebra isn’t just for middle and high schoolers.
Keywords: Connections, Activities
Ref: Becca13
Author(s): Ameis, Jerry A
Date: January, 2002
Title: Stories Invite Children to Solve Mathematical Problems
Journal or Publisher: Teaching Children Mathematics
Volume, Issue, Pages: 8(5), p. 260-264
Reviewer: Becca
Date of Review: 4/2/03
Children enjoy being read to and told stories. This can be vital to a classroom culture of problem solving. Many become engaged in important processes of reasoning and explaining as they learn about numerical relationships. Storytelling within the classroom setting can introduce a second aspect of problem solving as well. It can provide a meaningful context that motivates children to solve problems embedded in it.
The setting of the experiment took place at an after school daycare center. The research involved four boys and seven girls, all in elementary school. The purpose of the study was to investigate how children might be engaged in math problem solving under difficult conditions. The daycare setting offered a way to investigate this under conditions where the influence of schooling was unlikely to be a factor. Ameis struggled the first few times he visited the daycare center. He wasn’t seen as a teacher figure, children were free to choose whether or not to participate on a given Friday afternoon and there were many distractions coming from other children at the daycare not involved in the study. Needless to say, however, by the fourth session, Ameis decided to create and read a fantasy adventure story with routine and non-routine math embedded in it. Kids were quickly becoming interested in the story. As time went on, their participation and enthusiasm increased.
The power of storytelling for engaging children was evident in the daycare setting. The question then becomes, how can this carry over into the classroom? One good solution is that teachers can read appropriate books that have math in them. Another idea is to have children write their own stories that contain math in them. That way, students are involved in the creative side of the project, something that many would enjoy doing.
I think that storytelling is a wonderful way of getting students engaged in the material. It gives them something to become interested in while, at the same time, having to do math. I think it also allows students to retain the material more. A student is more likely to remember a specific math skill if they learned while reading a story that they enjoyed. I think this is definitely a technique in which needs to be implemented more into the classroom setting.
Keywords: Geometry, Technology,
Ref: Becca12
Author(s): Zheng, Tingyao
Date: October, 2002
Title: Do Mathematics with Interactive Geometry Software
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: 95(7), p. 492-497
Reviewer: Becca
Date of Review: 3/19/03
The subject of geometry involves a lot of mathematical generalization, the Pythagorean Theorem is just one example. The emergence of interactive geometry software enables students to discover relationships and patterns and make generalizations. When interactive geometry software, Geometer’s Sketchpad, for example, is available in the classroom, the teacher can adopt a different approach to solving problems whereas without this interactive software, students may have more difficulty understanding and making those connections. Math is a science of pattern. To draw any conclusion about a pattern, one has to make generalizations. The process begins with observation and speculation, continues with conjecturing, hypothesizing and verifying and proving. It concludes with generalizations at a higher level. The use of interactive geometry makes this process much easier for students to do.
I think that doing geometry using interactive software is a great way to learn. I really believe that being able to see what is being talked about makes a world of difference in understanding concepts and having to make connections and using interactive software is a great way to do that.
Keywords: Curriculum
Ref: Becca11
Author(s): Lott, Johnny W. editor
Date: January, 2001
Title: www.nctm.org/dialogues/2001-01
Journal or Publisher: Mathematics Education Dialogues
Volume, Issue, Pages: p. 1-20
Reviewer: Becca
Date of Review: 3/17/03
In the United States, integrated curricula have become the new thing of many school-reform programs. It has either been viewed as the savior of the curriculum or has been put down. In this issue of Dialogues, the essays that I read came from both people for and critics of integrated mathematics. However, I found that more often than not, the people writing the essays were in favor of the integration of mathematics in the classroom.
A lack of knowledge of new content and different pedagogy have become principal negatives for many schools that are considering adopting an integrated math program. Many critics point out that few current teachers are prepared to handle the curriculum and as a result end up teaching what is called fuzzy mathematics. Sarah Theule Lubienski, one of the only writers who seemed to be against the integrated approach, believes that one way in which real-world problems become the center of the curriculum is though the integration of several subjects. She says that when the integrated approach becomes the staple of math, and is implemented so that a single idea is rarely given focus, then the students have difficulty building any deep math understandings.
Although many of the writers discussed advantages to the integrated curricula, Hugh Burkhardt discussed them the most in detail. He believes that the main advantages of integrated curricula are that they build essential connections, help make math more usable, avoid long gaps in learning, allow a balanced curriculum and support equity. The usefulness of math depends greatly on making connections with practical contexts. Burkhardt states, “Students develop such “applied power” over practical problems only by using their math successfully in increasingly challenging problems, an activity that is possible only in a well-integrated curriculum.” It is obvious that there are many advantages to integrated curricula, but the question is, do you think they outweigh the disadvantages?
I thought this collection of essays about the issue of integrated curricula was extremely interesting. I never really understood exactly what it was and being able to read people’s opinions regarding the advantages and disadvantages of it was very informational. I find myself feeling like and integrated curricula is an overall positive approach, but as I learned by reading these essays, I have very limited information and must learn more about it before I form a strong opinion.
Keywords: Geometry, Activities,
Ref: Becca10
Author(s): Geddes, Dorothy
Date: 1992
Title: Curriculum and Evaluation Standards for School Mathematics Addenda Grades 5-8
Journal or Publisher: National Council of Teachers of Mathematics
Volume, Issue, Pages:
Reviewer: Becca
Date of Review: 3/12/03
The basic purpose of this particular book is to address issues and concerns about teaching and learning geometry and spatial thinking in relation to implementing standards into the classroom. It presents some different approaches to some geometry topics and provides a collection of sample activities, many of which are hands-on and fun! The examples are designed to develop students’ intuitive sense of geometry concepts, to foster higher-order thinking and to help students to value the role of geometry and reasoning in our society.
This is a really great resource for teachers to use for such a variety of activities within a geometry unit or class. Activities within it include building triangles with pipe cleaners, constructing pyramids and angles, exploring cubes, and discovering patterns, just to name a few. I would definitely recommend this to any math teacher to use as a tool in their teaching. The activities are great ways to get students excited about math by doing hands-on things and discovering lots of new ideas about geometry!
Keywords: Activities, Standards,
Ref: Becca9
Author(s): Hynes, Michael
Date: 1996
Title: Ideas: NCTM Standards-Based Instruction
Journal or Publisher:
Volume, Issue, Pages:
Reviewer: Becca
Date of Review: 3/10/03
This book a great resource that is full of different standards-based activities, most hands-on and real world applicable, to give students. Each activity provides the objectives, directions, materials needed and questions to ask students along with a student activity sheet. The activities vary in the subject matter as related to math, ranging anywhere from geometry to statistics.
Rock ‘r Rap is just one of the many activities in the book. The objective of the activity is to define a problem and ask a well-defined question that could be answered by means of data collection, to conduct a survey and display the data by multiple methods, and to interpret bar graphs in writing. To do this, students are supposed to use the activity sheet as a guide. They begin by deciding which type of music they think is the most popular in their class. They then are to survey their classmates and tally the results on the graph on the worksheet. Another graph is to be made to distinguish girls and boys and their music choices. A discussion will also take place just talking about how the results can be interpreted, the magnitude of this class’s range of preferences in music and so forth.
I think this is an extremely useful resource for math teachers. It gives so many different kinds of activities and ideas that are fun to implement into the classroom and states the objective of each one for you! I definitely would recommend it to any math teacher to use.
Keywords: Communication
Ref: Becca8
Author(s): Strutchens, Marilyn
Date: April, 2002
Title: Multicultural Literature as a Context for Problem Solving: Children and Parents Learning Together
Journal or Publisher: Teaching Children Mathematics
Volume, Issue, Pages: 8(8), p. 448-454
Reviewer: Becca
Date of Review: 3/5/03
In recent years, the math community has given more attention to the role that math plays in our cultural society. Multicultural literature offers a context in which readers can celebrate their own culture while, at the same time, learn about others. The Literature/Math program is one of the Math: Application and Reasoning Skills (MARS, a program of the Baltimore City Public School System) project’s mechanisms to help parents become aware of the changes that occur within math education thought literature of different cultures, adult-child pairs or families solve math problems. The program is 90 minutes once a week for six weeks.
The books used in the program represent several ethnic and socioeconomic groups and are appropriate for multiple grade levels. The program consists of two major components, a read-aloud portion and a problem-solving portion. During the read-aloud part, as a facilitator reads, he or she asks questions that are related to the stories that help make connections to the characters involved and also asks mathematical questions related to the text. During the problem-solving portion, parents and children are given a series of math questions that build on the context of the story. As a result, families learn different types of strategies (guess and check, making charts, drawing pictures, etc.) and as they present solutions, facilitators ask questions to help reflect upon their experience. This allows parents to be exposed to the types of questioning they can use at home with their children.
There are many benefits of this program. First, parents work collaboratively with their children. Second, families are introduced to a variety of cultures while learning math problem-solving skills at the same time. Third, parents begin to understand that rote memorization is not the only way to learn math. Fourth, the lines of communication about students’ math education are opened up for parents and teachers. Last, but certainly not least, parents and children become excited about doing math together.
This seems like a great idea to get parents involved in learning math with their children. I like how there is a multicultural aspect as well. I don’t doubt that this is a great program that is extremely successful, but I wonder how many people actually attend it since it isn’t something that is part of a normal school day. I feel like this is something that needs to be integrated into the schools all over the country because it is so important.
Keywords: Teaching Strategies
Ref: Becca6
Author(s): Sun, Wei; Zhang, Joanne Y.
Date: 2001
Title: Teaching Addition and Subtraction Facts: A Chinese Perspective
Journal or Publisher: Teaching Children Mathematics
Volume, Issue, Pages: 8(1), September, p. 28-31
Reviewer: Becca
Date of Review: 2/26/03
This article examined how Chinese math educators deal with finding unique approaches to teaching basic addition and subtraction and compared it with the American way. The Chinese clearly and consistently highlight the grouping-by-ten nature of our numeration system. For example, fourteen is “ten-four,” or thirty is “three-ten.” This structure easily leads Chinese children to view two-digit numbers as tens and ones. On the other hand, English counting terms are less explicit and consistent in revealing this base-10 nature of our number system.
The way Chinese and Americans teach addition and subtraction is very different. U.S. teachers often use counting in a one to one correspondence to introduce addition and subtraction. As a result, children rely heavily on this counting-based concept. However, in China, teachers use a three-step method. First they develop an understanding of number concepts. They learn the meanings of and the relationship between addition and subtraction. Second, they master addition and subtraction facts by breaking it into parts. They learn facts up to 10 first, where counting is emphasized. Next they learn facts between 11 and 2 where related subtraction facts are emphasized. Finally they learn facts between 20 and 100. During the last step, students are introduced to the addition and subtraction algorithms. This step by step process used by Chinese educators allows students to really learn and understand how to add and subtract as opposed to simply rely on counting to figure it out. “When using thinking strategies to perform addition and subtraction, students reinforce their understanding about the facts that they have learned by using those facts repeatedly” (p. 31).
In my experience, I find that students in the U.S. really struggle with their basic math skills such as addition and subtraction. Students really do rely way too much on counting with their fingers to figure out a simple math problem because they haven’t really actually learned and understood it. The Chinese method seems to be a very in-depth approach that works and allows students to fully understand these basic skills. I think the U.S. should consider changing their way of teaching addition and subtraction to something similar to the Chinese. Although their way of teaching may take longer because more steps are involved, students would benefit so much more in the long run.
Keywords: Technology
Ref: Becca7
Author(s): Flores, Alfinio
Date: February, 2002
Title: Learning and Teaching Mathematics with Technology
Journal or Publisher: Teaching Children Mathematics
Volume, Issue, Pages: 8 (6), p. 308-310
Reviewer: Becca
Date of Review: 3/3/03
This article talked about how technology can potentially alter the way that children learn math and the way teachers and schools conceptualize its teaching. In the elementary grades, technology can be used to enhance a concrete, experimental approach to math topics, which enables students to have greater success with a more abstract approach later on.
However, the impact of technology on learning has been slow. Calculators really aren’t used much in the elementary classrooms. Computers aren’t integrated as part of the regular learning experience in math and the Internet is often restricted to the point it makes it impractical for teachers to use.
How to incorporate technology into the classroom can be quite a challenge because you must decide when it’s appropriated and you need additional support of trained people to help you plan, maintain and coordinate the use of it. Equity is another important issues. The use of technology becomes difficult when some districts have few resources available to them. Technology brings plenty of advantages to the classroom and can enhance a student’s education greatly, it just must be used in the appropriate manner.
I thought this article addressed some important issues as related to technology in the classroom. It is crucial that you don’t let technology take over your class, but at the same time, are able to integrate it in enough to enhance the learning environment. Technology seems to be quite a hot topic in education and I am interested in reading more about it.
Keywords: Teaching Strategies
Ref: Becca6
Author(s): Sun, Wei; Zhang, Joanne Y.
Date: 2001
Title: Teaching Addition and Subtraction Facts: A Chinese Perspective
Journal or Publisher: Teaching Children Mathematics
Volume, Issue, Pages: 8(1), September, p. 28-31
Reviewer: Becca
Date of Review: 2/26/03
This article examined how Chinese math educators deal with finding unique approaches to teaching basic addition and subtraction and compared it with the American way. The Chinese clearly and consistently highlight the grouping-by-ten nature of our numeration system. For example, fourteen is “ten-four,” or thirty is “three-ten.” This structure easily leads Chinese children to view two-digit numbers as tens and ones. On the other hand, English counting terms are less explicit and consistent in revealing this base-10 nature of our number system.
The way Chinese and Americans teach addition and subtraction is very different. U.S. teachers often use counting in a one to one correspondence to introduce addition and subtraction. As a result, children rely heavily on this counting-based concept. However, in China, teachers use a three-step method. First they develop an understanding of number concepts. They learn the meanings of and the relationship between addition and subtraction. Second, they master addition and subtraction facts by breaking it into parts. They learn facts up to 10 first, where counting is emphasized. Next they learn facts between 11 and 2 where related subtraction facts are emphasized. Finally they learn facts between 20 and 100. During the last step, students are introduced to the addition and subtraction algorithms. This step by step process used by Chinese educators allows students to really learn and understand how to add and subtract as opposed to simply rely on counting to figure it out. “When using thinking strategies to perform addition and subtraction, students reinforce their understanding about the facts that they have learned by using those facts repeatedly” (p. 31).
In my experience, I find that students in the U.S. really struggle with their basic math skills such as addition and subtraction. Students really do rely way too much on counting with their fingers to figure out a simple math problem because they haven’t really actually learned and understood it. The Chinese method seems to be a very in-depth approach that works and allows students to fully understand these basic skills. I think the U.S. should consider changing their way of teaching addition and subtraction to something similar to the Chinese. Although their way of teaching may take longer because more steps are involved, students would benefit so much more in the long run.
Keywords: Must Select At Least One, Standards,
Ref: Becca4
Author(s): Stepanek, Jennifer
Date: 1997
Title: It's Just Good Teaching
Journal or Publisher: Science and Mathematics Standards in the Classroom
Volume, Issue, Pages:
Reviewer: Becca
Date of Review: 2/19/03
This 30-page book talked a lot about the math and science standards and that they were created in response to concerns about the performance of students. The standards provide clear goals for students and teachers and outline what students should know and be able to do. These standards were based on constructivist theories or learning and recognize the fact that students learn in many different ways and at different rates.
The five general goals for the standards are as follows: 1. learn to value math 2. become confident in one’s own ability 3. become a math problem solver 4. learn to communicate mathematically 5. learn to reason mathematically Ways of achieving these goals and integrating this new approach into classrooms is not going to be an easy process. Teachers must really examine the standards and reflect on their own teaching to see how or if they parallel with each other. A positive learning environment in which all students and the teacher feel comfortable is essential as well. Teachers should discuss strategies, what works and what does not, with their peers and use them as a resource for ideas.
I thought this was a really informative book that enabled me to understand more of the details
behind the new constructivist approach and the standards that go along with it. It’s a great
resource to look at for some ideas on how to begin to integrate it into the classroom as well as
developing yourself into a better teacher.
Keywords: Teaching Strategies
Ref: Becca5
Author(s): Williams, Susan E; Copley, Juanita V.
Date: 1994
Title: Promoting Classroom Dialogue: Using Calculators to Discover
Patterns in Dividing Decimals
Journal or Publisher: Mathematics Teaching in the Middle School
Volume, Issue, Pages: 1(1), April 1994, p. 72-75
Reviewer: Becca
Date of Review: 2/24/03
This article was an example of a change in teaching strategy that developed to take advantage of the use of calculators. The activity took place in Mary Lynne’s 6th grade classroom. The topic was looking at patterns when dividing decimals and Mary Lynn’s concern was when to use the calculator during the lesson. During the first class, she began with some examples (272.6/58, 2.726/58, 27260/58 and 2726/58) and asked students what was the same and what was different without being able to use their calculators. Students were confused so she brought the whole class together and they were finally able to identify some patterns and rules about the movement of the decimal point. She then allowed them to use their calculators to verify their predictions. After class, she decided that the objective wasn’t meant and decided to try something different with the next class.
This time, students were allowed to use calculators right away and investigate the question posed in the beginning of the first class. Mary Lynne found that students caught on a lot more quickly and were more excited about the patterns. It sparked a lot of great questions that she hadn’t even thought of. Overall the second class went a lot better, even though both classes learned something. The second class was just more active in the learning process than the first.
This activity concluded that when students are encouraged to experiment and ask questions, they are able to construct a deeper understanding of the material. Not only that, but calculators can supply the computations power that is often needed to discover patterns when working with numbers.
I thought this was a good article showing how different a class period can go when you change something up in the way you present it to the class. Although learning did take place in both sessions, it was obvious that the second one was a lot more productive because she allowed students to investigate with their calculators right from the beginning and sparked many questions from students. It just makes me realize that you must be aware of all parts of your lesson and be willing to reflect on what worked and what didn’t and change it accordingly.
Keywords: Teaching Strategies, Standards,
Ref: Becca3
Author(s): Ward, Cherry
Date: 2001
Title: Under Construction: On Becoming a Constructivist in View of the
Standards
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: 94 (2) p. 94-96
Reviewer: Becca
Date of Review: 2/17/03
Teachers have taught math in the same way, with very little variation, despite instructional trends for a very long time. A lot of the educational movements never really became widely accepted by teachers. But, there is a recent alternative to traditional instruction that is emerging. The National Council of teachers of Mathematics (NCTM), who performs the service of determining the efficacy of various methods, promotes this recent alternative called constructivism.
Constructivism is the idea that by building on previous knowledge, students are able to grasp the concepts better and can actually understand the material as opposed to simply learning it. It is a critical thinking approach that seems to be a successful one. However, with this approach the teacher plays an important role. He or she must offer additional situations to test the student’s knowledge and must also understand that student’s constructions may differ from their own. Another important aspect of this idea is the communication between teacher and student. It is essential because otherwise the teacher will not know how the student’s knowledge has been constructed. This idea seems to offer promising new approaches to teaching, but it definitely is going to be a challenge.
I thought this article was very informative and introduced an idea that I had never heard of. I
think that trying to change the way math is taught is something that is necessary and really like the
idea of constructivism. It seems like a great approach that seems to be working so far. It is
definitely something that we all can learn from and can begin to think of ways we, as future
teachers, can implement into
Keywords: Curriculum
Ref: Becca1
Author(s): Butterworth, Susan; Lo Cicero, Ana Maria
Date: 2001
Title: "Storytelling: Building a Mathematics Curriculum from the Culture of
the Child"
Journal or Publisher: Teaching Children Mathematics
Volume, Issue, Pages: 7(7), p. 396-399
Reviewer: Becca
Date of Review: 2/10/2003
This article was centered around the idea and belief of Reggio Emilia that a successful curriculum grows from the child’s own interests and that a child’s experience is most meaningful if the culture that each child brings from home is connected with activities in the school setting. This uses children’s own stories for teaching and learning in the classroom. This project approach, “seeks to create a common culture of the children as a group by working from the stories that each child brings from the culture of his or her homes” (p. 397). The specific project described in this particular article involved the students going with their parents to the supermarket. They then had to re-enact the experience at school and share it with their peers. The teacher’s role is to look for opportunities to turn the children’s stories into word problems while the main purpose is to teach relationships (ex. food products and money in this case).
I thought this was a great approach that should really be used more. Not only is it a fun
and active way to learn, it also brings the diversity of the students and their experiences into the
classroom.
Keywords: Curriculum, Activities,
Ref: Becca2
Author(s): Civil, Marta; Khan, Leslie
Date: 2001
Title: Mathematics Instruction Developed from a Garden Theme
Journal or Publisher: Teaching Children Mathematics
Volume, Issue, Pages: 7(7), p. 400-405
Reviewer: Becca
Date of Review: 2/12/03
This article spoke of a garden theme that one teacher, Leslie Khan, used in her classroom. She decided it would be a good way to allow students to explore the interplay between everyday knowledge and school math. The theme began in Khan’s classroom when she had a “Curriculum Night and Open House” to introduce the idea to her students’ parents. The parent’s response was a positive one.
Students began developing their gardens and experiences related to the garden theme lasted for five months. They nurtured plants, kept garden journals and brought information and resources from home to share with classmates. As this process was taking place, Khan and her students began identifying situations that required mathematics. For example, math was needed to determine the volume of soil, the amount of soil to buy or the height of the plants. These are just a few of the ways math was used during this garden experience.
I felt that this was an extremely creative and fun idea to bring into a math classroom. It really shows students how math can be related to just about anything. It also allows students to implement math, a subject they might not care for, and apply it to something they are interested in. I think it’s a great idea that also gives students some responsibility. A garden isn’t something that’s easy to care for. Having the responsibility to take care of it and record everything in a journal is something students can and should learn at an early age. Overall I feel that this is a great way to get students excited about learning math.