Keywords: Teaching Strategies, ,
Ref: Terrazas1
Author(s): Banchoff, Thomas F.
Date: 2000
Title: "The Mathematician as a Child and Children as
Mathematicians"
Journal or Publisher: Teaching Children Mathematics
Volume, Issue, Pages: Vol. 6, Number 6
Reviewer: Terrazas
Date of Review: 3/16/00
This article discusses the importance of young children having the opportunities to develop their "mathematical minds" and how teachers play a big role in doing this. The author recounts how his general curiosity and interest in dimensions and shapes led to his love of mathematics. Growing up, the author writes, his mother encouraged him to ask questions and this carried over into his education. He was lucky enough to have math teachers who allowed him to ask questions and explore mathematical concepts on his own so that he may discover what they mean on his own. This developed his mathematical mind to the point where he could easily identify relationships or patterns and think in those terms.
Young math teachers must realize how important discovery learning
and hands-on activities are in mathematics and give students a
chance to figure mathematical concepts out on their own.
Furthermore, teachers need to encourage kids to ask questions and
help them find the answer or explore different possible answers
to their questions. It is also important to go beyond the
textbook in mathematics and search for questions, answers and ways
to teach using alternative means like computers and even comic
books. This article can definitely be applied in our future
teaching careers when we will be working with potential
mathematicians. By taking the authors advice, we will also have
the opportunity to develop our students as mathematicians and make
mathematics much more enjoyable for them.
Keywords: Research, ,
Ref: Terrazas2
Author(s): Hiebert, James
Date: 2000
Title: "What Can We Expect from Research?"
Journal or Publisher: Teaching Children Mathematics
Volume, Issue, Pages: Vol. 6, Num. 7, pp. 436-7
Reviewer: Terrazas
Date of Review: 3/21/00
In his article , Hiebert discusses the proper application and use of education related research. The article stresses the importance of research as a tool for making decisions, or informing the decision makers, and developing guidelines to improve mathematics education. For instance, it can supply information about how to design an effective classroom environment. In our case, it gives people confidence in the decisions that are made about mathematics educations.
However, research does have its limitations and this is what the author is
warning against. Research can provide evidence and helpful clues, but as
Hiebert writes, the best one for all people and for all time (437).
Basically, it
cannot dictate the proper materials, methods or values applied to
mathematics education. These decisions need to be made based on the kind
of mathematics valued by particular schools, communities and societies.
Hierbet concludes the article with three guidelines he feels can be
applied universally to mathematics education:
1) what they have an opportunity to leanr;
2) to engage directly in the kind of mathematics they are to leanr;
3) skill proficiency (437).
Keywords: Teaching Strategies, Algebra, Problem Solving
Ref: Terrazas3
Author(s): Nathan, Mitchell J.; Koedinger, Kenneth R.
Date: 2000
Title: "Moving beyond Teachers' Intuitive Beliefs about
Algebra Leearning"
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: Vol. 93, Number 3, pp. 218-223
Reviewer: Terrazas
Date of Review: 2/22/00
The standard belief among teachers, in this case, algebra teachers,is that story problems are one of the most difficult tasks that their students face. Likewise, students generally find story problems the least desirable and, therefore, they are usually placed at the end of the lesson. However, Nathan and Koedinger researched these ideas and came up with results that suggests those algebra teachers have the wrong perceptions of story problems and that students really have nothing to worry about when it comes to these tasks. This is because high school algebra students who participated in this study did somewhat better on algebra story problems than they did with just the arithmetic.
Nathan and Koedinger suggest students did better on the story problems because they were free to use what ever method they wanted to solve the problems. Some students were able to solve these problems the way most math teachers would desire, by setting up equations and doing the arithmetic. Students also had the liberty of using methods such as "guess and check" and the "unwinding strategy." So, students who couldn't do the arithmetic had other options.
The article suggests that teachers should not be reluctant to incorporate story problems in their lessons. If students can begin to solve the problems informally, the use and understanding of the formal strategies can be built upon this. Furthermore, it will provide another tool by which to teach the students the arithmetic necessary to solve these problems.
Math, obviously, is a very difficult subject to understand,
especially as students move into algebra. I was surprised by the
results of the survey, too. Story problems seem like more work
and I think this perception is what makes them so difficult when
they really aren't. I think it is important to recognize this
about story problems so that teachers are aware of how valuable
they can be and how they can use them as a teaching tool even
when students don't understand the arithmetic.
Keywords: Communication, Teaching Strategies,
Ref: Terrazas4
Author(s): Steele, Diana F.
Date: 2000
Title: "Enthusiastic Voices from Young Mathematicians"
Journal or Publisher: Teaching Children Mathematics
Volume, Issue, Pages: Vol. 6, Number 7, pp. 464-468
Reviewer: Terrazas
Date of Review: 4/3/00
Diana Steele's article, "Enthusiastic Voices from Young Mathematicians,"
examines communication and teaching strategies used for problem solving
in elementary mathematics. To do so, Steele examined several elementary math
classes and talked to the teachers to find out how elementary school children
thought in comparison to mathematicians. She found similarities in how the
children reacted or responded to new mathematical ideas and also how they
communicated their mathematical ideas to their peers. The implications
of Steele's research include a very important role for teachers in
dialogue amongst their students mainly by presenting situations or ideas
and asking questions of their students, their ideas and solutions.
Furthermore, the opportunity to "recreate" mathematical concepts and
situations and apply what they have learned is important for students.
Keywords: Activities, Games, Teaching Strategies
Ref: Terrazas5
Author(s): Gaglione, Jeffrey T.
Date: 2000
Title: "Relay Review"
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: Vol. 93, Number 4, pp. 282-3
Reviewer: Terrazas
Date of Review: 4/5/00
Gaglione stresses at the beginning of his article that when his students leave his math class at the end of the year he wants them to understand the relevance of math and to have had fun. To do this, he plays a number of review games in class and one of them is called revie.w He divides his class into groups of even ability levels and gives each team a set of questions to work on as a group. The students sit in a row and starting with the first person, they go up to a chalkboard to do their problems while their teammates help them from their seats. As each person gets done with their problem, the pass thei r to the next person who must go up to the board with the next question. It is kind of like a relay in track.
This game is an excellent review activity and could be extremely fun,
especially if prizes are involved. It is also very flexible in terms of
the questions used, time, and group sizes. It also provides an
opportunity for students to work in groups and help each other learn the
material instead of having the teacher give a lecture or do problems on
the board. Gaglione also plays music, such as the anthems of various
countries, to give the game an Olympic touch. He has had a great amount
of success with it.
Keywords: Activities, ,
Ref: Terrazas6
Author(s): Binongo, Jose Nilo G.; Smith, M. W. A.
Date: 2000
Title: "Project Jacobean: A Mathematical Exploration of a
Literary Era"
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: Vol. 93, Number 4, pp. 338-343
Reviewer: Terrazas
Date of Review: 4/7/00
Project Jacobean was thought up by a high school AP Calculus teacher who wanted to give his students a unique mathematical experience. The object was to apply calculus in a field where few people would expect to see it, literature. Furthermore, the teacher wished to get his students to derive their conclusions without the help of a textbook or known equations and answers, similar to what mathematicians experience centuries ago.
By using graphs, deriving equations and patterns of word choice and word
type in various literary works by known authors, the students doing this
project were to identify the author and era of a n literary
work. The project was a big hit among the students and an excellent
year-end activity. The project was a little more difficult than it sounds
and probably suited best for more advanced high school students.
Nonetheless, it is an excellent idea, reward and break for the students in
this AP Calculus class who spent the year getting ready for the AP test.
Keywords: Gifted, Algebra, Teaching Strategies
Ref: Terrazas7
Author(s): Feigenbaum, Ruth
Date: 2000
Title: "Algebra for Students with Learning Disabilities"
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: Vol. 93, Number 4, pp. 270-4
Reviewer: Terrazas
Date of Review: 4/10/00
Feigenbaum's article addresses a growing concern of how to provide a proper education to students with learning disabilities. Several accommodations have been made for these students over the years, but they are insufficient. Also, according to Fiegenbaum, schools and school counselors put little confidence in these students and do not provide them with opportunities to access and learn algebra.
To solve this problem, the author suggests programs such as the one at
Bergen Community College. At Bergen Community College, special care is
taken to classify and accommodate more students with learning
disabilities. BCC has created a special algebra class for LD students to
fulfill their special needs and restructured teaching and learning
strategies used in its classes. The outcome has been very successful and
the article definitely makes some good points on how to accommodate all
your students in any class.
Keywords: Activities, Statistics,
Ref: Terrazas8
Author(s): Durkin, Marilyn B.
Date: 2000
Title: "Using Financial Headlines and the Internet to Keep
Statistics Classes Fresh"
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: Vol. 93, Number 4, pp. 318-323
Reviewer: Terrazas
Date of Review: 4/10/00
The activity idea Marilyn Durkin provides in her article is one that would fit perfectly in one of the Integrated Math curriculums we have taken a look at in our class. Students are required to monitor the stock market, Dow Jones industrial average, and how the stocks of specific companies do in comparison to the DJIA. The progress of these various components are then graphed in comparison to each other. In doing this, the students are required to work with a variety of types of graphs to find the correlations. Students also must work on computers and they get valuable experience in applying mathematical relationships to real life.
This activity would be an excellent introduction and on-going
activity to conduct in a unit on statistics. The depth into
which Durkin takes this activity is definitely suited more for an
upper level high school class or for older students (for example
an FST class meaning sophomores or juniors) who could probably
understand the information better and would have more interest.
However, it could easily be adapted for younger students.
Nonetheless, it sounds like an excellent activity and one I will
definitely consider.
Keywords: Teaching Strategies, ,
Ref: Terrazas9
Author(s): Andrade, Heidi Goodrich
Date: 2000
Title: Using Rubrics to Promote Thinking and Learning
Journal or Publisher: Education Leadership
Volume, Issue, Pages: Vol. 55, Number 5, pp. 13-18
Reviewer: Terrazas
Date of Review: 4/16/00
This article discusses how value of using rubrics as instructional tools. Andrade refers to these as "instructional rubrics." Good instructional rubrics are easy to use and explain. They make teacher expectations clear and provide students with more informative feedback about their strengths and areas in need of improvement. The article claims instructional rubrics to this better than traditional forms of assessment. Furthermore, they support learning, development of skills, understanding and good thinking abilities by seeking out and promoting thinking centered around criteria. And finally, test score have showed that students who use rubrics to assess themselves learn more.
This article does not seek to get rid of traditional forms of assesment,
but the use of instructional rubrics in addition, I believe, will help the
students. They will learn how to assess themselves and have a better idea
of what is expected.
Keywords: Tests, ,
Ref: Terrazas10
Author(s): Hoff, David J.
Date: 2000
Title: Test Scores May Be Misleading, Experts Warn
Journal or Publisher: Education Week
Volume, Issue, Pages: Vol. 19, Number 30, pp. 10
Reviewer: Terrazas
Date of Review: 4/16/00
We've all learned in our previous education courses that we cannot base the intelligence and achievement of our future students completely on standardized test results. This article also warns against relying on standardized test scores as signs of achievement and progress in our education system. The reasons include that kids are getting more familiar with and better at taking these tests. Also, instruction is changing to focus on the tests and not what they represent. Finally, test scores do not tell what is happening in the classroom.
Better indicators of achievement and progress would be monitoring the increase in the number of students in challenging classes and improvements of student work. According to Hoff, having teachers aim their instruction at the test will be detrimental to the education system. He is not recommending that the tests be done away with, but asks that the technology available be used to provide a wider range of questions and make the changes quicker, along with fixing other short-comings.
Hoff is right, test scores can be misleading, but it is a much more simple
way to monitor our education system and compare students and progress on
local, national and world scales. This is probably why Hoff does not ask
that the tests be done away with. However, as teachers, we will have to
look much deeper than the test scores of our students to monitor their
progress and ours.
Keywords: Standards, ,
Ref: Terrazas11
Author(s): Hoff, David J.
Date: 2000
Title: "Math Revisions Add Emphasis on Basic Skills"
Journal or Publisher: Education Week
Volume, Issue, Pages: Volume 19, Number 31, pp. 1,19
Reviewer: Terrazas
Date of Review: 4/25/00
According to this article, NCTM is getting ready to reveil its latest
revision of the standards. Criticism that the original standards put too
much emphasis on new ideas causing some teachers to miss the main goal
("to become highly skilled in using mathematics") led to these latest
revisions. According to the article, the message behind the standards
will stay the same, but it will do a better job of outlining what skills
students should master in each four-level grade band and expand the focus
on basic skills.
Keywords: Standards, ,
Ref: Terrazas12
Author(s): Easton, Lois E.
Date: 2000
Title: "If Standards are Absolute. . ."
Journal or Publisher: Education Week
Volume, Issue, Pages: Volume 19, Number 31, pp. 30,32
Reviewer: Terrazas
Date of Review: 4/25/00
This article is written by Lois Easton who is a teacher at Eagle Rock
School in Estes Park, CO. Eagle Rock is a school that handles kids who
have given up, dropped out of school or failed out of other schools. She
shares some of her ideas and techniques used at Eagle Rock in working with
these students. She points out that achievement in schools used to be a
variable and time and place, curriculum, learning style and assessment
techniques were absolutes. Easton says to make achievement absolute, the
goal that the education is shifting toward, schools must make the former
"absolutes" variables. She describes how this is done at her school.
Keywords: Connections, Geometry,
Ref: Terrazas13
Author(s): Natsoulas, Anthula
Date: 2000
Title: Group Symmetries Connect Art and History with
Mathematics
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: Volume 93, Number 5, pp. 364-370
Reviewer: Terrazas
Date of Review: 5/9/00
This article discusses the use of art, architecture and weaving patterns from
Ethiopia, Cyprus and other cultures as tools to connect history and art
with the underlying themes of algebra and geometry. These designs are
actually very mathematical involving transformations and reflections, the
"six mathematical activities" (counting, locating, measuring, designing,
playing and explaining) and the basic axioms of algebra (closure,
identity, inverse and associativity). These patterns and designs can be
used to demonstrate symmetry, rotation and reflection. In more advanced
math classes, the students can get more in-depth and discuss these
patterns in terms of mathematical groups and create their own to
illustrate group symmetry. Using these patterns and designs offers a
concrete image for some abstract concepts that many students have
difficulty with. This would be something good to explore if a teacher
ever some extra time to implement an activity involving these patterns.
Keywords: Activities, ,
Ref: Terrazas14
Author(s): McGlone, Chris; Nieberle, Gary M.
Date: 2000
Title: Using Hooke's Law to Explore Linear Functions
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: Volume 93, Number 5, pp. 391-8
Reviewer: Terrazas
Date of Review: 5/9/00
This activity deals with Hooke's Law to study the (linear)
relationship between stretch and force for springs and
rubberbands. It looks like a pretty simple activity to implement,
too. Students use various types of candies place in a paper cup,
attached to a spring or rubberband, to test how the force applied
stretches the rubberbandor spring. Students then graph the data
and find a line of best fit that should approximate a linear
relationship. This activity is a good discovery learning tool to
introduce students to linear relationships, finding the line of
best fit and its equation, solving that equation for different
amounts of applied force and stretch and correlation. We did a
similar activity in one of my high school math classes. I can say
from experience that the students will probably have fun doing
this activity and it is an excellent teaching tool.
Keywords: Research, Algebra,
Ref: Terrazas15
Author(s): Manzo, Kathleen Kennedy
Date: 2000
Title: Algebra Textbooks Come Up Short in Project 2061
Review
Journal or Publisher: Education Week
Volume, Issue, Pages: Vol. 19, number 34, pg. 5
Reviewer: Terrazas
Date of Review: 5/12/00
The American Association for the Advancement of Science set up Project 2061 in an attempt to improve math and science education. To do this, they reviewed 12 of the most widely used Algebra textbooks and evaluated them on their usefulness for math students and teachers. Unfortunately, Project 2061 found five of these Algebra books do not build students knowledge of math and do not build a deeper understanding of mathematical concepts.
These Algebra books (Algebra 1: Explorations and Applications; Algebra 1: Integration, Applications, Connection; Algebra: Tools for Changing Our World; CORD Algebra; Integrated Mathematics: A Modeling Approach using Technology) received a rating of "poor" or "fair." Seven of these books, however, where graded "adequate" for doing a satisfactory or good job of building a sequence of activities, providing practice and meeting some of the NCTM Standards.
I think this is a valuable article to take a look at, especially as we
head out into the teaching world and my be dealing with some of these
curriculums.
Keywords: Standards, ,
Ref: Terrazas16
Author(s): Manzo, Kathleen Kennedy
Date: 2000
Title: N.J. Standards Beginning To Alter What Is Taught, But
Not How
Journal or Publisher: Education Week
Volume, Issue, Pages: Vol. 19, number 34, pg. 7
Reviewer: Terrazas
Date of Review: 5/12/00
The good news in this article is that the new math standards and
curriculum are beginning to change what is taught in mathematics classes
for the better. The bad news is that the methods and how math is being
taught is not changing. This is especially true in poorer school
districts. The author calls attention to the difficulty in changing
pedagogy and believes that professional development options are inadequate
for doing this. This is a problem that must be addressed for the new
standards to reach their potential.
Keywords: Teaching Strategies, ,
Ref: Terrazas17
Author(s): Sutton, Suzanne
Date: 1996
Title: Math: One of Life's Big Pluses
Journal or Publisher: The Washington Post, August 19,
1996
Volume, Issue, Pages: www.suzannesutton.com/post.htm
Reviewer: Terrazas
Date of Review: 5/12/00
Sutton talks about a common fear other people that we'll all address as
teachers: math. This is unfortunate because math occurs all around us and
is involved in many of the things we do. As teachers, it is very
important that we do everything possible to make our students comfortable
with math. This can be difficult and will test our patience because math
can be a complex and complicated language and intimidating. Sutton offers
four suggestions to help teachers make math a more pleasurable experience
for students: 1) As a teacher, reconsider and expand your view of what
math is; 2) Encourage the process of discover and reasoning; 3) Permit
exploration; 4) Praise the child. It's a very good article that is well
worth reading.
Keywords: Teaching Strategies, Communication,
Ref: Terrazas18
Author(s): Crow, Tracy
Date: 2000
Title: Involving Families by Exciting Kids
Journal or Publisher: Eisenhower National Clearinghouse
Volume, Issue, Pages:
www.enc.org/focus/topics/family/articles/a06/index.htm
Reviewer: Terrazas
Date of Review: 5/14/00
This article focuses on ways teachers can involve their students'
families in their education. Building the enthusiasm of your students in
hopes that the enthusiasm will "go home" with them to their parents is one
way to do this. New teaching methods, projects and activities are simple
ways to do this. Communication between teachers and parents proves very
valuable, too, in Crow's experience. She found that most parents respond
well to new ways of learning and teaching math and it is valuable to keep
them informed. Crow does this by sending out a weekly newsletter, holding
family math nights and encouraging volunteer work in the class. Parents,
obviously, play a very important role in a child's education and they can
be very valuable models to their children when it comes to how they do
their work.
Keywords: Assessment, ,
Ref: Terrazas19
Author(s): Nataro, S. Leigh
Date: 2000
Title: Statewide Portfolio Assessment in Mathematics:
Journal or Publisher: Eisenhower National Clearinghouse
Volume, Issue, Pages:
www.enc.org/focus/topics/assessment/articles/a08/index.htm
Reviewer: Terrazas
Date of Review: 5/14/00
Mathematics problem solving and communication cannot be assessed meaningfully on standardized tests. This concerned a group of Vermont teachers. In response to their concerns, these Vermont teachers developed a successful statewide portfolio assessment system. Students compile portfolios of their work at the end of fourth, eighth and tenth grade and assessed on a local and statewide level. On the statewide level, a random sample is taken to take the emphasis off individual and school achievement and put it on statewide achievement. The portfolio system is working well in Vermont and encouraging professional development among teachers who must meet certain standards to be eligible to "grade" the portfolios.
Vermont is a small state (in population and size) and this really helps
this system work. Nataro believes this system could work well in other
states, too. It would need some help, though. Support for the change
needs to come from everyone with a stake in our children's education:
government officials, higher education leaders, K-12 teachers,
administrators, and parents.
Keywords: Teaching Strategies, ,
Ref: Terrazas20
Author(s): Stine, Mary Ann
Date: 2000
Title: State Achievement Tests Can Be a Positive Force in
Your Classroom
Journal or Publisher: Eisenhower Clearinghouse
Volume, Issue, Pages:
www.enc.org/focus/topics/assessment/articles/a12/index.htm
Reviewer: Terrazas
Date of Review: 5/14/00
This article discusses how a Washington elementary math teacher used the Washington State Essential Academic Learning Requirements as an opportunity as opposed to a roadblock with her math classes. To often, teachers who have little faith in them or see them as an obstacle to overcome in their classroom and teaching methods criticize the new curriculums and achievement standards imposed by different states. Stine saw an opportunity to used these new standards to create a better math curriculums and learning environment for her students and develop herself professionally.
Stine and her colleagues researched, examined, and developed lessons they thought reflected the new learning requirements. After teaching those lessons, they spent more time discussing pedagogy and assessment. This team planning time with her colleagues was one of the most valuable aspects of their development of reform-based classrooms.
Eventually, Stine's students began to view the classroom as a place that fostered open, sincere communication. The new skills and processes Stine and her fellow teachers used created a classroom where effective learning occurred and students developed skills that reached beyond the classroom. Also, Stine and the other teachers were able to use a wider variety of assessment to gather better, valid information about their students' understanding of math.