Keywords: Teaching Strategies, Algebra
Ref: Lauren1
Author(s): Choike, James R.
Date:
October 2000
Title: ALGEBRA for All
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: Volume 93, No. 7, p. 556-560
Reviewer: Lauren
Date of Review: February
15th, 2004
This article talks about different "algebra-for-all" strategies that are helpful when teaching math in general, but specifically algebra. The first strategy is to emphasize the big ideas of algebra rather than to focus on the little things. Choike says that since algebra is really only made up of a few conceptual themes, focusing on these themes will help all students connect new and old topics and it will give a conceptual framework for the course without being bound to follow the book.
The next strategy is to eliminate numbers as distracters to understanding new concepts. Choike points out that a lot of times books give problems using decimals rather than whole numbers when first introducing a new concept. He suggests that instead the numbers should be switched to easier numbers so students can focus on the idea of the problem rather than just the numbers. Along with this idea, the next strategy is the ensure entry into a new problem. A lot of the time the wording of the problems is another thing that can confuse students. Choike suggests to avoid using ambiguous terms and other words students may not understand so they can again just focus on the problem and not try to figure out what the problem means.
The next algebra-for-all strategy is to emphasize multiple representation. When solving a math problem many different strategies can be used and Choike talks about how important it is that students can use and apply all of these strategies such as using words, tables of data, graphs, and symbols. Another strategy is to revisit rich or popular settings, which means to go back and revisit old problems and to try and change them a little so that a new concept can be learned from an old, familiar problem. He also suggests using situations that are popular with students as this will also increase the interest level for doing a new type of problem. In addition, Choike talks about how it is beneficial to mold lessons around the interests of individual students in order to increase interest.
Another strategy is to not begin the year by remediating. Choike argues that this takes away valuable time and that it is better to just "jump right in" to the new curriculum and use warm-up activities or a small portion of a lesson to review the things that need to be reviewed, rather than setting aside a few weeks for review.
The next strategy Choike talks about is to involve students in guided exploration. This way students will stay engaged in the lesson and they will begin to think about math in their own way. Similarly, it is important to recognize correct thinking in students even when it may be incomplete or lacking in closure, meaning that as teachers it is important to encourage students if they are on the right track or even close to being on the right track. Math is a subject where students can get discouraged very easily, so it is important to keep encouraging them every step of the way.
Finally it is
important, in any classroom, to establish a safe classroom
environment. Students are unable to focus and to learn if
they do not feel as though they are safe and as though they
are able to ask questions and give their opinions.
Keywords: Geometry
Ref: Lauren2
Author(s): Buhl, David A.
Date: April 2001
Title: Missing Pennies and Eating Pi
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: Volume 94, No. 4, p. 254-257
Reviewer: Lauren
Date of Review: February 17th, 2004
This article talks about yet another way to describe the number pi. Students in Buhl's college geometry class were faced with the question, Will a seventh penny placed in the center of the circle formed by the coins be tangent to all six coins?
Once they d discovered it was true for pennies, they tried to see if it was true for any coin, different numbers of coins, etc. One student then discovered that the ratio of the number of coins over the radius of the inner circle converges to a number close to pi. Then, after more calculations, the class discovered that by letting the radius of each outside circle equal 1, the limit of this ratio is equal to pi.
I think it is really cool how this teacher used this problem to create a cool unit for his students. Just by presenting this one problem, the students came up with numerous cool observations.
Keywords: Teaching Strategies......
Ref: Lauren3
Author(s):
Date:
Title: Math Portal Home: Middle School Lesson Plans-Go Fish
Journal or Publisher:
Volume, Issue, Pages: http://fcit.usf.edu/math/lessons/activities/GoFishT.htm
Reviewer: Lauren
Date of Review: 2-22-04
Overall I think that this lesson does a good job of addressing the eight components of a lesson plan. This lesson is titled "Go Fish" and it teaches students about figuring out the sample in a population by having them do an experiment using goldfish crackers and proportions. The goals and the objectives of the lesson plan are stated at the top. The state standards which this lesson addresses are at the top as well. By the end of the lesson students should understand data collection, how to interpret data, and how to use proportional reasoning. They also should know how to solve proportions.
The materials or tools that each group will need are clearly listed on the lesson plan as well. This lesson also includes a "hook" section in which the teacher presents an activity that should get the students attention. In this lesson the hook activity suggests an ineffective way that you could catch and tag fish, but the students should then realize that it is not a good idea and they should want to think of a better idea, which is the whole idea of the lesson. The lesson procedure is laid out in a very detailed way, and I think that anyone would be able to follow the instructions without a problem.
Although there is not a specific closure, I think that one could use the "analyze the data" section for the closure activity. The assessment section could also be used where the students need to answer questions about when the procedure could be used and about factors that may influence the results. In either case, I think that one of these activities could be used for an appropriate closure because the students are forced to reflect on and think about what they just did. For the extension the author of this lesson plan included a math connection section which says that students will now be able gather information about a large sample whose makeup is similar. Therefore, students can use what they learned and apply it to other math problems or maybe even a science problem.
In general I think that the is a really good lesson plan. It addresses all of the parts to a lesson plan and it does so in a way that the students can get involved. I think that students would learn really well from this lesson and I definitely think that I would use this lesson in my own classroom.
Keywords: Activities, Teaching Strategies...
>Ref: Lauren4
Author(s): Berry, Stephanie M.
Date: September 2002
Title: Students Realize Mathematics is Everywhere
Journal or Publisher: Teaching Children Mathematics
Volume, Issue, Pages: Volume 9, Number 1, p. 9-15
Reviewer: Lauren
Date of Review: 2-29-04
This article was really enjoyable to read. It was about how Stephanie Berry, a fifth-grade teacher, used the book "Math Curse" by Jon Scieszka as a way to help her students learn to appreciate math. She began by reading the book to the class. The students were then assigned to create their very own "Math Curse" book by using their experiences throughout the day. The students were to create their book using at least ten word problems. Before turning in a final copy, students held conferences with each other so that they could make sure that all of their answers were correct. Once the final copy was finished, the students were given the opportunity to display their books at the local Barnes and Noble bookstore. Berry said that it usually takes about four weeks since it is such a big project. She said that the students get really into it and that they work hard to make the best book possible.
Personally I think that this unit is a fabulous idea. I absolutely love this book and I really think that students would learn a lot by doing this. From a teacher standpoint, I think that this project is ideal because each student is able to work at his or her level and create ability appropriate problems. More advanced students can take it to the next level and create books for different periods of history or for different culture or countries. Students are able to be creative and to use real-life applications to see how math is relevant in everyday life. Students also get the opportunity to work on language arts and art stills, as well as getting the opportunity to publish a book in its entirety. It is a long term project, and I think that students will gain confidence and feel a great sense of accomplishment once it is over. As I said earlier I think that this project would be awesome and I can't wait to try it out in my own classroom!
Keywords: Standards......
>Ref: Lauren5
Author(s): Collins, Edna Neal; Skipper, Edith L
Date: March 2003
Title: Making the NCTM Standards User-Friendly for Child Care Teachers
Journal or Publisher: Teaching Children Mathematics
Volume, Issue, Pages: Volume 9, Number 7, p. 421-427
Reviewer: Lauren
Date of Review: 2-29-04
This article talked about how hard it is for some early childhood and child care center teachers to read and understand the standards that are to met by preschoolers. In order to help improve this situation, the University of North Carolina-Wilmington ran a Math Enhancement Project at 12 child care centers. The first assessment was to have somebody perform a checklist of the materials that were found in the classroom. The second was a survey that was completed by the teachers that asked about the current level of mathematics in the classroom. Then, the university looked over the information and came up with areas that were to be targeted during six different visits. During these visits, math specialists would go into the classrooms and model appropriate activities that the teachers were to be doing with their students to help them meet the standards. In addition to these visits, the teachers were instructed to attend three workshops where they were taught more about things that they could do in the classroom to increase the mathematical activities. The teachers were also taught about how to use different resources in the classroom as well as how to use parental involvement to help stimulate math knowledge.
Overall, the project was a huge success, even though it was only done in 12 centers. All of the teachers reported a huge increase in their comfort level with mathematical terms as well as how to use these ideas and terms to help get their students ready for kindergarten. This definitely seems like it is a problem, and hopefully things like this can be done all over so that all preschool teachers and early childhood teachers feel confident enough and comfortable enough to teach these mathematical concepts.
Keywords: Problem Solving, Teaching Strategies...
>Ref: Lauren6
Author(s): Buschman, Larry
Date: October 2002
Title: Becoming a Problem Solver
Journal or Publisher: Teaching Children Mathematics
Volume, Issue, Pages: Volume 9, Issue 2, p.98-103
Reviewer: Lauren
Date of Review: 3-7-04
In this article, Larry Buschman describes his seven stages that he believes children go through during their development of becoming problem solvers. He came up with these seven stages using classroom observations, one-on-one interviews, and scored work samples. He identifies the first stage as the concrete stage where children need to solve the problem using actual objects or actually going through the motions so they can arrive at a solution. During this stage students will be able to solve the problem, say the answer, but not necessarily write be able to write the answer down. The next stage according to Buschman in the readiness stage. In this stage students use resources, like fingers to count objects, that are readily available to them. Students in the readiness stage still have difficulty explaining how they arrived at a solution, even though it is the right solution.
The next stage, the copying stage, is when children use traditional classroom materials to keep track of abstract thoughts. Once again, they have a hard time verbalizing their solution, but they can "show" their solution using the classroom manipulatives. During the next stage, the mechanical stage, children will turn to exact representations and drawings of the problem and the solution to come to the right answer. They still lack verbal communication, but like in the copying stage, they can "show" their solution using their drawings.
Buschman's next stage is the novice problem-solver stage and this is when students can use trial-and-error and they can try several different methods of solving the problem until they find one that works. In addition, students do not need exact drawing of the actual objects. Instead they can begin to incorporate a variety of symbols and letters to solve the problem. This is also the first stage where students are able to verbalize their solutions using drawings and oral descriptions. The apprentice problem-solver stage is the next stage and this is when students use abstract drawings gs to solve the problem. They are also able to write solutions to problems using the correct mathematical terminology and they are able to include almost all of the steps they took to arrive at their solution. The final stage, the problem-solver stage, is where students can represent the problem using abstract symbols. In addition, they can completely describe their solution process and they can solve the problem in more than one way. They understand their solution and why it works.
I think that this article is really important for teachers to read. It gives a detailed overview of the various stages that a child could be at with problem solving. Not all students are going to be at the same level and it is important to be able to recognize that fact and use that to make sure that all students are working up to their potential.
Keywords: Probability, Teaching Strategies...
>Ref: Lauren7
Author(s): Lanier, Susie; Barrs, Sharon
Date: December 2003
Title: Let's Play Plinko: A lesson in Simulations and Experimental Probabilities
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: Volume 6, Number 9, p.626-633
Reviewer: Lauren
Date of Review: 3-7-04
This article talked about how using the game Plinko from the Price is Right can teach students about probabilities. The teacher made a Plinko board and used it to show students the differences between theoretical and experimental probabilities. The students then each did a trial and they found that the experimental probability was 10%, where the theoretical probability 11.5%.
Next, since they only had one trial for each student (20 trial) they developed a program on a TI-83 so that they could further investigate this game. After the students did 1600 simulated trials, they found that the experimental probability was 11.7%, which is much closer to the theoretical probability. By doing so, students were supposed to understand that for the more trials used, the better the experimental probability would be.
I think that this activity is a great way to teach students about probability. Plinko is something that almost everyone knows about and it is something that is fun and interesting. By using something like this, students see how math is used in the everyday world.
Keywords: Statistics, Teaching Strategies...
Ref: Lauren8
Author(s):
Bratton, George N.
Date: November 1999
Title: The Role of Technology in Introductory
Statistics Classes
Journal or Publisher: The
Mathematics Teacher
Volume, Issue, Pages: Vol. 92, No.
8
Reviewer: Lauren
Date of Review: 3-14-04
This article talks about how beneficial the use of technology can be in introductory statistics classes. Anyone who as taken a statistics class knows how tedious some of the calculations can be. Therefore, in this article, Bratton discusses the idea that students can learn so much more of the bigger picture if they can avoid having to do all of the calculations and memorization of the formulas. By doing so, Bratton argues that three things happen: it makes teaching some topics unnecessary, it permits teaching some topics better, and it allows teaching some topics that have never been taught.
The main unnecessary topic that Bratton talks about are the numerous paper and pencil computations. He says that with the use of computers and calculators students can avoid having to do these computations and can then just analyze the results. When teaching the principles of early statistics, Bratton feels that it is more important to be able to understand the results, as opposed to actually memorizing the formulas and being able to plug in the numbers. THerefore, with the use of computers and calculators, teachers can avoid spending time forcing students to memorize the formulas, which frees up more time that can be spent teaching new topics.
Bratton's second point, teachers can increase the time spent teaching other topics, stems from students not having to do the numerous calculations. With the use of technology, students can analyze several different trials and large sample sizes within minutes. Without computers and calculators this process would takes forever, but now students can just press a button and tons of data is right there. This allows students to further investigate the data and to draw conclusions about the "big" ideas of statistics without having to do all of the busy work.
In addition, because students do not have to spend countless hours doing calculations and with the use of new technology, teachers also have the time and the resources to teach new topics that have never b een taught before. Some current new topics that are being covered are ANOVA and SPC hypothesis testing. Both of these topics are fairy new in the field of statistics and they both involve inclusion to the real world, which is great for students.
In conclusion, Bratton emphasizes that statistics used to be a course filled with tedious arithmetic computations and the memorization of many formulas, but not anymore. With the use of technology in the classroom, students are no longer faced with doing all of the arithmetic, they now can look at the "big picture." The shift of the teaching of mathematics is leaning towards this direction, and the use of technology in statistics classroom is definitely a step in the right direction.
Keywords: Problem Solving, Standards, Teaching
Strategies
Ref: Lauren9
Author(s): Williams, Kenneth M.
Date:
March 2003
Title: Writing about the
Problem-Solving Process to improve the Problem-Solving Performance
Journal or Publisher: The Mathematics Teacher
Volume, Issue, Pages: Vol. 96, No. 3, p. 185-187
Reviewer: Lauren
Date of Review: 3-15-04
In his article, Kenneth Williams reports the findings of a study that involved the comparison of having students actively reflect about the problem solving process with not reflecting at all. As indicated in the NCTM standards, problem solving is a process that involves understanding the problem, devising a plan, carrying out the plan, and looking back at the problem. In this study, 42 beginning algebra students were split up into a treatment group and a control group. The students were then given a pretest and a posttest, and the results were then analyzed.
Both groups were taught the same things by the same teacher. Aside from their regular assignments, both groups were given five challenging problems a week. The control group would just try the problems and hand them in while the control group would have to write a paragraph or two describing the processes they used and/or any difficulties they had while attempting to solve the problem.
Not suprisingly, at the end of the study, the treatment group had significantly more success and improvement with the problem solving process. Therefore, this study proves that it is beneficial for students to be actively responding and reflecting to what they are doing. Doing so helps students gain a better and deeper understanding of each problem and the problem solving process in general. Contrary to popular belief, writing is an extremely important part of math that can have a significant positive effect on a students performance and overall understanding of math.
Keywords: Curriculum, Standards...
Ref: Lauren10
Author(s): Geddes, Dorothy
Date: 1992
Title: Curriculum and Evaluation Standards for School
Mathematics
Journal or Publisher: National Council of Teachers of
Mathematics
Volume, Issue, Pages: Geometry in the Middle Grades
Reviewer: Lauren
Date of Review: 3-30-04
The main objective for the Curriculum and Evaluation Standards books is to provide teachers with numerous examples and problems on how to implement the standards into their classrooms. The ideas, examples, problems, and activities in the books show how to meet the standards using an integrated approach that touches on the five mathematical processes. Back when the standards were published in 1989, this whole concept of teaching was very new. Therefore, this series helps to guide teachers in how exactly to teach that way. Teachers had to learn how to become the facilitator instead of just the presenter of information.
The Geometry in the Middle Grades book deals specifically with geometry and how to meet those standards using the new approach of teaching. The book provides many wonderful examples, problems, and activities that use all of the five mathematical processes. The problems are all very different and they use a variety of different means. All of the activities are very hands-on and they all are very relevant to what is being taught. Throughout the whole book, there are also numerous helpful teaching tips. Everything is laid out very nicely for the teacher in a way that makes a lot of sense.
Overall I thought that this book was great. It addresses a lot of
important ideas using all of the mathematical processes. As a teacher,
I know I would feel comfortable using this book and I think that
students would definitely be able to learn using the many different
activites and problems.
Ref: Lauren11
Author(s): Fernandez, Maria L.; Anhault, Cynthia O.
Date: December 2001
Title: Transition toward Algebra
Journal or Publisher: Mathematics Teaching in the Middle
School
Volume, Issue, Pages: Volume 7, No. 4, p. 236-241
Reviewer: Lauren
Date of Review: 3-30-04
This article talked about the significance of teachers' views on algebra and how that affects getting students ready for algebra. During a two-year project called the Transition Toward Algebra project, teachers of grades 5-9 helped to develop ways to enhance the development of algebraic thinking for their students. They did so by actually experiencing algebra themselves through hands-on problems. The teachers would meet for a month long time period in the summer where they would solve problems and share their thoughts, strategies, and results in hopes that it would expand their views of algebra and algebraic thinking. The project wanted teachers to think of algebra as the study of patters and relationships, as a tool for problem solving, and as generalized arithmetic, and not just as solving equations with variables.
As a result of the project, teachers did indeed expand their views of algebra and algabraic thinking. During the project, teachers were able to use many different ideas and representations. Thus, the teachers also realized the importance of having students use problem solving in order to better understand mathematical concepts. In addition, teachers were taught how to develop more engaging problems that dealt with a broader definition of algebra.
In the end, the Transition Toward Algebra project was a huge
success. In my opinion, what made this project so successful was the
fact that the teachers actually had to go back and do algebra problems.
Doing so forced teachers to see and to realize the importance of doing
problem solving and using different representations to help students
better understand a mathematical concept. The group collaboration was
extremely important as well. As a result, teachers were able to see a
variety of different methods and thinking strategies, very similar to
those of their students. Not all students see a problem the same way,
so it is crucial that teachers foster a learning environment in which
all students can do math in a way that makes sense
to them.
Keywords: Number and Operation, Activities...
Ref: Lauren12
Author(s): Miller, Catherine B.; Veenstra, Tamara B.
Date: January 2002
Title: Beautiful Patterns, Beautiful Mathematics
Journal or Publisher: Mathematics Teaching in the Middle
School
Volume, Issue, Pages: Volume 7, Number 5, p. 298-305
Reviewer: Lauren
Date of Review: 3-30-04
This article talks about different activities that teachers can use to teach students about the Fibonacci sequence. First, the article suggests to have students find the Fibonacci sequence in nature. For instance, it occurs in the number of swirls on a pinecone, and in the arrangement of petals in some flowers. Next, the article suggets that together as a class you should try and decipher why exactly the pattern does occur in nature (i.e. optimal packing of the seeds, the relationship to the golden ratio, etc).
The article also provides three wonderful worksheet activities that allow students to really study the Fibonacci sequence and its different characteristics. The first worksheet just has students try to figure out the pattern of the Fibonacci sequence as well as how to label the different entries of the sequence. The second worksheet goes a little deeper by having students figure out the relationships between the Fibonacci numbers and the different multiples. The third worksheet is more advanced as it has students make a conjecture about he greatest common factors of any two Fibonacci numbers.
In my opinion, all three worksheets are wonderful. They all have
students go through and fill out tables to try and figure things out,
as opposed to just telling students about the different patterns and
characteristics. It is a very integrated approach that I think would
really help students to understand why the different characteristics
exist. I would definitely use the worksheets in my classroom!
Keywords: Representations, Standards...
Ref: Lauren13
Author(s): Preston, Ronald V.; Garner, Amanda S.
Date: September 2003
Title: Representation as a Vehicle for Solving and
Communication
Journal or Publisher: Mathematics Teaching in the Middle
School
Volume, Issue, Pages: Volume 9, Number 1, p. 38-43
Reviewer: Lauren
Date of Review: 4-13-04
This article talked about the importance of students using different representations to solve a problem. Seventh-grade prealgebra students were given a problem where they had to decide which class party plan would be best. Students worked in groups of three-five students and they were able to solve the problem any way that they wanted. Almost all of the groups used some sort of graph to try and figure out which plan would be best, but groups also used word rules, tables, patterns, and even equations.
Students found that graphs were helpful in showing people their results, tables were a good organizational tool, and equations were a good summary statement of their findings. Doing this problem helped students to see many different graphs and why some worked better than others. At first students were a little skeptical to use equations, but after a little convincing from the teacher, students began to see that using equations is a good, compact way of expressing their results.
One thing that the teacher mentioned was that when students are able to choose their own representation, sometimes students choose one that is the most familiar to them, not one that makes the most sense. Therefore, the teacher suggests, if you want to teach a specific representation you should do a model problem first and then have students apply what they just learned. Students think is such different ways that teachers cannot expect students to think how they think.
All of the techniques that students used were good problem solving techniques, yet some worked better than others. However, doing this activity helped students to see why this is true. Students were also able to see why using equations to represent graphs is so helpful. Overall I think that representation is a crucial part of mathematics. As a teacher, it is important to create a classroom where all different types of representations are used. Not all students think the same way and this needs to be supported in the classroom.
Keywords: Geometry, Teaching Strategies...
Ref: Lauren14
Author(s): Bell, Clare V.
Date: November 2003
Title: Learning Geometric Concepts through Ceramic Tile Design
Journal or Publisher: Mathematics Teaching in the Middle School
Volume, Issue, Pages: Volume 9, Number 3, pp. 134-140
Reviewer: Lauren
Date of Review: 4-21-04
In the
introduction to this article, Bell emphasizes the importance of ceramic tiles and their designs to different
cultures. So aside from the math, this lesson also deals with multiculturalism. The connection between
math and multiculturalism is almost nonexistent, so finding a lesson that connects the two is very
important. Since the students actually make their tiles, this also helps to illustrate that math really is used in
the real world. Overall, I really think that this unit will teach students a lot about math and geometry, as
well as about other cultures.
Keywords: Teaching Strategies, Curriculum...
This article talks about the difficulty that the author, Sarah Browman, had when she switched from
45-minute class periods everyday to block scheduling, one 70-minute class period every other day. When
Browman first made the switch she assumed that she could just cover twice the material and assign twice
the homework. Boy was she wrong! The students were becoming extremely restless and overwhelmed and
Browman knew that something needed to be done. After doing a lot of research, Browman found that
she needed to adapt her old lessons to the longer class period by breaking them up into several smaller
activities. She also found that it was helpful to include different types of assessment such as journal
writing, portfolio entries, and projects. In addition, the research indicated that students in block scheduling
needed both social interaction and movement to stay engaged throughout the whole class period. Browman
found that the lessons should include at least three different activities as well. With the help of her
research, Browman began to plan her lessons based on this format: 5-10 minute warm-up activity, 15-20
minutes of homework review, 20 minutes for an introduction to the new topic, 20-25 minutes for a group
activity, 15-20 minutes of skill practice, and 5 minutes for a wrap-up discussion. Within this model, she
used a lot of flexibility and variety by changing how the different activites were completed everyday.
Browman feels that thus far this schedule has been very effective. She says that her students are much
more engaged in the lesson because they are actively involved throughout the whole lesson. Incorporating
two simple things, movement and social interaction, into a daily routine can make a huge positive impact in
the overall classroom environment.
Keywords: Equity/Diversity, Standards, Teaching Strategies
This article talks about ways to apply the Equity Principle in a middle
school classroom. The Equity Principle states that "Excellence in mathematics
education requires equity-high expectations and strong support for all
students." This may seem like it would be simple, yet even basic things can
lead in inequity. First, Gilbert aruges that even just calling on students
who raise their hand leads to inequity because this only allows for a few
students to share their answers with the class while the rest of the class does
not get involved. SHe suggets labeling popsicle sticks with each students name
and then picking one each time you need a student to either answer a question or
volunteer. This way each student is held responsible for themselves and each
student will have the opportunity to participate an equal amount of time.
Similarly, Gilbert talks about the importance of group work and assigning roles
within the groups. This, again, makes sure that each group member is held
accountable and is able to have equal say. She also suggests a "jigsaw"
technique where groups become experts on a topic and then teach the rest of the
class about thier topic. In addition, Gilbert uses team roles in her groups and
she has students rotate so that all students are able to have each role.
Another thing that is important to Gilbert is empowering her students as
knowers. She does this by encouraging her students to find answers on their own
and not just relying on her to give them the answers. Because of this, Gilbert
feels that her students are more willing to take risks and figure things out on
their own. In order to get rid of the typical stereotypes associated with
math, Gilbert has a bulletin board titled "Women's Work" that teaches students
about famous women mathematicians and scientists. She finds that all students
respond positively to this because most students are already aware of the famous
males. Another Gilbert does to help achieve equity in her classroom is to
recognize and
welcome students' realities in her classroom. She teaches in a diverse school,
so it is important for her to understand her students' lives as well as the
lives of their parents. Gilbert also tries to directly apply problems to her
students lives. She feels that by doing so her students become more involved in
the problem and more motivated about math. Overall, I feel that Gilbert is
doing a wonderful job of creating equity in her classroom. In this article she
discusses some very good ways to do so. It is easy to forget that doing simple
things, like calling on students who volunteer, does actually promote inequity.
All students need to feel safe and feel that they are being treated equally in
order for the classroom to be a successful learning place.
Keywords: Teaching Strategies, Activities...
I attended Jim's Talk, Putting the "F" word Back in Math...Fun!, at the
Minnesota Spring Mathematics Conference in Duluth on April 30th and May 1st.
The talk was fabulous and I received several wonderful ideas for activities.
The talk was geared for k-2, but the activities could easily be adapted to upper
elementary as well. He began his talk by saying that 30% of students are
visual learners, 20% are auditory learners, and 50% students are kinesthetic
learners. This was really surprising to me, but it makes perfect sense. Based
on this, Jim tries to teach math using as much movement as he can. One example
of how he does this is by having students do times test like they are playing
musical chairs. He will put a song on and the kids will have to start working
on their tests, once the music stops they have to move and find another chair
and start working on that test. If someone finishes, the next person then has
to go back and check the answers and make sure they are all right. Jim says
that the students really love this activity because they are able to be up and
moving. Another activity that he talked about was having students jump on
either lilly pads or coins to practice either adding or subtracting. Sometimes
he will even have his students jump all the way down to the lunch room! Once
again he said that this was a really good activity because students are able to
do math and move around at the same time. Another thing that Jim does is he
uses gummy bears or another concrete object for every aspect of math. He said
that his students very rarely just do problems or worksheets without actually
"doing" whatever it is that they are working on. He keeps tons of gummy bears
on hand at all times so that his students can use them for adding and
subtracting. He also gave the idea of taking jello and putting it on a cookie
sheet to help students either practice math facts or spelling words. The
students can then be rewarded by being able to eat the gummy bears or licking
their finger
from the jello. While we were at the talk, Jim actually had us do a lot of
the activities. When we first started he had us do the musical chair activity
so that we could see how it worked. He also passed out gummy bears and teddy
grahams and allowed us to play around with them. Overall, I really enjoyed his
talk. He provided many wonderful ideas and activities and he really gave me a
new understanding of how to incorporate movement and math in my classroom.
Keywords: Teaching Strategies, Curriculum...
I attended Michelle's talk, Using Children's Literature to Enhance Middle
School Mathematics, at the 2004 Minnesota Spring Mathematics Conference in
Duluth. When I first saw what talks were available, this was one that was at
the top of my list because I think that it really is important to try and
incorporate math and literature whenever possible. During her talk Michelle
focused on how to use picture books to teach her 8th graders about math. At
first I was a bit skeptical as to if 8th graders would really be wanting to look
at picture books, but Michelle says that it works extremely well and that her
kids love using the books. She focused a lot of the Sir Cumference book series,
which is something that I was unfamiliar with before this talk. She actually
read the book to us and pointed out all of the math that it is involved, which
is actally a lot! Michelle also gave us a sample worksheet that she uses with
her class. The students have to go through the book and pick out certain things
about the circumference and then use that information to see if the book is
valid. It seemed like a really good way to teach students about circumference
and I can see how students would really get involved. In addition to the
tons of picture books that she introduced, she talked about how to incorporate
novels with math. The main one she focused on was "The Giver" by Lois Lowry and
how it could be used with probability. Having just read "The Giver" for
children's literature, it was really fun for me to see that it definitely can be
used with math. Most people, myself included, would probably not think of it as
being a math book, but it is. Michelle said that she has her students find the
probability of actually having a perfect community of 25 girls and 25 boys every
year and the probability of having light eyes, etc. A lot of 8th graders read
this book so I think that it is great that aside from it being a good book, it
can be used for math as well. Overall, I really enjoyed Michelle's talk.
Besides just talking about all of the wonderful benefits of using literature
to teach math, she showed us how to exactly do so. She also gave a wonderful
book list that I will definitely be using in my classroom!
Keywords: Probability, Statistics, Teaching Strategies
When I was at the 2004 Minnesota Spring Mathematics Conference, I
attended a talk, Probability and Statistics in Grades 3-5, gived by Karen
Holstein and Denise Anderson. Karen and Denise teach in the same district,
which is just starting to use the Navigation Series as a supplement to their
regular text books. Having seen and looked at this series during class, I was
really interested to see some of the applications of this book. Their talk
focused on how to teach probability, statistics, and data analysis in grades 3-
5. They first had us do an activity in order to collect data. We had to
draw as many stars as we could in one minute. Once we had our data, they had
each of us write it on a post-it note. We then had to construct a box-plot
graph out of the post-it notes. I really thought that this was a good idea.
Creating an actually graph out of the post-it notes is a good way for students
to see and be able to comprehend the data in a concrete way. Also, since the
students have to actively construct the graph, it gets all students involved.
Both Denise and Karen have made graphs on the first day of school as a way to
introduce data analysis and to get to know the students. Both of them also said
that a lot of teachers will collect data, but will then not really analyze it.
The Navigation Series, however, places a lot of emphasis on analyzing data,
which they both feel is really important. An easy way to analyze the data
once it is made into a graph, is to look at the shape of the data, and look for
bumps, clumps, holes, outliers, and the range. When they first introduced these
terms I was not 100% sure what they all meant, but once they explained them it
made perfect sense. Having students look at all of these things really helps
they to get a strong understanding of the graph and the different trends of the
data. It also really helps students to see and explain why the mode, median, or
mean could be affected by these characteristics. In terms of probability,
they had us construct a probability line with the words impossible, unlikely,
equally likely, likely, and certain. We then had to decide where the numbers,
0, 1/2, and 1, would belong on the line. Once again, both of them said that
they have had students do this and that students really like the activity and
that they really understand what everything means. In addition they asked us
several questions and what the probability was of each event occuring by having
us actually stand up and stand under the probability line at the correct place.
I thought that this was a really good idea too because it had us apply
probability to the real world. I think students would really like doing this as
well. Once again, this talk was very beneficial for me. Before attending
this talk, I never really thought of ways to analyze data or talk about
probability so that the students can be actively involved. I got many wonderful
activities and ideas that will be helpful to me once I become a teacher.
Subject:
WWW Form: articleinfo.form
From:
Nobody
Keywords: Assessment, Teaching Strategies, Keyword 3, Optional...
This article focuses on an alternative form of assessment called Standards-Based Assessment and Portfolios. It was developed as a result of the increasing lack of interaction between parents and students once students get older as well as because of the increased emphasis on grades and not on learning. Two teachers from Rice Lake, Wisconsin set out to change this by trying this alternative form of assessment. They began by designing two units based on the Wisconsin Model Academic Standards for Mathematics. Once they picked their units, they used basckwards designing and developed a standards-based assessment unit. They determined that the students needed to be learning the specific standards, so they then determined the evidence that would be used to make sure the objectives have been met. Next they decided how they would teach the unit and what materials were needed. Both of the teachers then implemented these plans in their classrooms. Throughout the units the students were constantly evaluating themselves and assessing their own knowledge and the learning that was taking place. When different assignments were returned students had to go back and attach comments so that they could demonstrate growth. Once the units were over, the students put together portfolios and brought them home and shared them with their parents. They had to sit down together and go over all of the work and then fill out a student/parent reflection sheet. Overall, the teachers felt that these portfolios accomplished their goals because it was a really good way to validate and document individual growth. The students were held responsible for what they were learning and they were then able to share this information with their parents, which the parents especially enjoyed. Even though there was a lot of success, the project did take a lot of time and effort and it was not always easy to assign students a letter grade for their work. In the end, however, this project proved to help students be aware of the l
earning that was taking place as well as increasing parent involvement, which was the intent.
Ref: Lauren15
Author(s): Broman, Sarah M.
Date: May 2002
Title: Making Minutes More Meaningful: 90 Minute Mathematics Class
Journal or Publisher: Mathematics Teaching in the Middle School
Volume, Issue, Pages: Volume 7, Number 9, pp.530-532
Reviewer: Lauren
Date of Review: 4-21-04
Ref: Lauren16
Author(s): Gilbert, Melissa C.
Date: September 2001
Title: Applying the Equity Principle
Journal or Publisher: Mathematics Teaching in the Middle School
Volume, Issue, Pages: Volume 7, Number 1, pg. 18-19,36
Reviewer: Lauren
Date of Review: 5-4-04
Ref: Lauren17
Author(s): Stang, Jim
Date: 2004
Title: Putting the "F" Word Back in Math...FUN!
Journal or Publisher: 2004 Minnesota Spring Mathematics
Conference
Volume, Issue, Pages:
Reviewer: Lauren
Date of Review: 5-12-04
Ref: Lauren18
Author(s): Reich, Michelle
Date: 2004
Title: Using Children's Literature to Enhance Middle School
Mathematics
Journal or Publisher: 2004 Minnesota Spring Mathematics
Conference
Volume, Issue, Pages:
Reviewer: Lauren
Date of Review: 5-12-04
Ref: Lauren19
Author(s): Anderson, Denise; Holstein, Karen
Date: 2004
Title: Probability and Statistics in Grades 3-5
Journal or Publisher: 2004 Minnesota Spring Mathematics
Conference
Volume, Issue, Pages:
Reviewer: Lauren
Date of Review: 5-12-04
Ref: Lauren20
Author(s): Chappell, Britton, Kristine L; Johannes, Jennifer L.
Date: October 2003
Title: Portfolios and a Backward Approach to Assessment
Journal or Publisher: Mathematics Teaching in the Middle School
Volume, Issue, Pages: Volume 9, Number 2, p. 70-76
Reviewer: Lauren
Date of Review: 5-22-04