Keywords: Statistics, Assessment, Teaching Strategies
Ref: Siverson1
Author(s): Watson, jane M
Date: 2000
Title: Statistics in context
Journal or Publisher: Mathematics Techer
Volume, Issue, Pages: Jan. 2000, Vol.93, Number 1, pg.54
Reviewer: Siverson
Date of Review: 04-07-2000
She says that by using examples from the media and natural setting that teachers can seek for students to have a high level of questioning skills of Judging statistical claims in social contexts is fundamental to statistical literacy in the world. In this article she is looking to help structure experiences to build abilities to question claims made without justification. She gives suggestions in a hierarchy form to help set out a structure to plan for and decide how to assess learning in this manner. It is broken into three areas as follows; 1) Understanding of statistical terminology in graphs and drawings. 2) Understanding of statistical language and concepts when embodied in context of another discussion, to be able to describe events that have reasoning in them. 3) A questioning attitude that can apply more sophisticated concepts to analysis and claims decisions. statistics and figures.
I think this is sort of obvious to any teacher, that real world
application might be a goal of ours. Well, duh. She makes a good point to
use media and natural statistics in lessons to place a real world
application to it.
Keywords: Geometry, Activities,
Ref: Siverson2
Author(s): Morgerm, Pat
Date: 1999
Title: An Old Tale with a New Turn- and a Flip and Slide
Journal or Publisher: Teaching Children Mathematics
Volume, Issue, Pages: Oct 1999, Vol 6, Number 2, pg 34
Reviewer: Siverson
Date of Review: 04-07-2000
Pat discusses using a story book format to gain interest of students
and do math while telling the story. The book he uses is called "Three
Pigs, One Wolf and Seven Magic Shapes." In it the three little pigs story
is shifted around to create other chances to introduce the Tanagram
shapes. They meet ducks and cats and stuff and the students are asked to
be creative and create those shapes out of the Tanagram Shapes. This
creativity and Problem Solving skill combination is just great. They then
describe the shapes and the manipulations they used to make them. The
mathematical language is developed and ingrained. Personally I hate
Tanagram Shapes (because I never could do them at all) but the opportunity
to give this to students and discover new things is great.
Keywords: Probability, Number Theory,
Ref: Siverson3
Author(s): Bay, Jennifer M, Reys, Robert E.
Date: 2000
Title: Bingo Games
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: March 2000, Vol. 93, Number 3
Reviewer: Siverson
Date of Review: 04-07-2000
Using the randomness of bingo this activity looks to examine
mathematical thoughts and premises that are formed while playing, like "it
will be easier to get bingo under the N." and other probability type
statements that can be made during a game. This includes things like
prediction, number sense and probability. The authors work out a number
of exampleused easily I feel to impress upon students the type of importance to
understanding of these statements in life and numbers.
Keywords: Communication, Assessment, Planning
Ref: Siverson4
Author(s): Nathan, Mitchel J., Koedinger, Kenneth R.
Date: 2000
Title: Moving Beyond Teacher's Intuitiv Learninge Beliefs
About Algebra
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: March 2000, Vol. 93, Number 3
Reviewer: Siverson
Date of Review: 04-07-2000
Are the beliefs teaches and students have about story problems being
difficult and bad really justified? The fact is that the beliefs that
teachers hold about students mathematical abilities and learning process
most influence teacher's pedagogical decisions, planning of activities,
and instructional practice. The article examines the teacher student
perception of abilities and sets them back to earth by realizing that when
giving the freedom to solve problems students never fail to surprise.
They claim, and I would agree, that in general arithmetic problems are
believed by teachers to be easier than algebra, symbolic and verbal
problems, regardless of format. When tested the students showed that the
first half was correct, but that many methods were used to solve symbolic
and verbal problems to get the correct answers. The author's claim at the
end is to build upon students
e.
Keywords: Connections, Teaching Strategies,
Ref: Siverson5
Author(s): Heuser, Daniel
Date: 2000
Title: Mathematics becomes learner centered
Journal or Publisher: Teaching Children Mathematics
Volume, Issue, Pages: Vol. 6 Number 5
Reviewer: Siverson
Date of Review: 04-19-2000
Daniel looks into connecting such things as writing workshops to math workshops with focus upon 1) choice, 2) time with manipulatives and 3) student reflection. The choice allows students to be active in whatever they are interested in at the appropriate level for them. Manipulatives help students visualize abstract ideas. He says the more actions that are done with manipulatives, then the better they are understood with symbols. The reflection helps students to construct meaning from their activities.
These concepts are met in the workshop through a short mini-lesson to introduce an idea, activity time for students to choose and work at discovery, and reflection time. The teachers role during activity time is to be and observer, questioner and communicator with students. To be sure activity time is not playtime rules need to be established with respect to what is expected in the reflection and have an emphasis on work.
I like the idea of being
learner centered rather than teacher centered. It is good for an activity
that could happen once a week perhaps, along with teacher centered
lessons.
Keywords: Geometry, Activities,
Ref: Siverson6
Author(s): Lehrer, Richard; Curtis, Carmen L.
Date: 2000
Title: Why are Some Solids Perfect?
Journal or Publisher: Teaching Children Mathematics
Volume, Issue, Pages: Vol. 6 Number 5, pg. 324
Reviewer: Siverson
Date of Review: 04-19-2000
This article describes how classification comes alive in a third grade
classroom as children searched for rules and properties for defining the
five Platonic Solids (solids that are polyhedra composed of regular
polygon regions with same number of faces at each vertex). Using
Polydrons, interlocking plastic polygonal pieces, students construct
solids and map them out in a two-dimensional surface that shows the
unfolded pattern. They are then encouraged to postulate ideas and test
them with other shapes. Sometimes this causes a modifying of the rules
that were postulated. Thus this activity (and ones like it) become an
outline for conjecture and experimentation for things about evidence and
proof. This also provides a great opportunity for discussion and other
modeling to happen.
Keywords: Communication, Issues, Teaching Strategies
Ref: Siverson7
Author(s): Stuart, Venessa B.
Date: 2000
Title: Math Curse or Math Axiety?
Journal or Publisher: Teaching Children Mathematics
Volume, Issue, Pages: Vol. 6 Number 5, pg. 330
Reviewer: Siverson
Date of Review: 04-19-2000
This teacher looks at why students feel relaxed and competent in math
while others find it nervous and stressful anytime they are confronted
with math questions. She says that their distress is more than a curse
but an affliction of math anxiety. The feeling of sudden death can
develop into math avoidance and math phobia. It is not the inability of
the person that gives them this feeling but it is their mental confidence.
The opportunity to work in groups lowers the anxiety and helps keep them
involved in class. Another tactic is to use manipulatives. She tried to
connect student views of math with parent views of math, but there was not
a god correlation. So it is up to the student to form their own idea of
what math is for them. As a teacher she says certain practices can also
help reduce this anxiety such as creating different testing environments,
make math relevant,
Keywords: Teaching Strategies, ,
Ref: Siverson8
Author(s): Williams, Nancy B; Wynne, Brian D.
Date: 2000
Title: Journal Writing in the Mathematics Classroom
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: Vol. 93 Number 2 pg 132
Reviewer: Siverson
Date of Review: 04-19-2000
In the world of new assessment and methods journal writing has made its
way in to the world of math. This article is an account of two teacher
who implement journal writing in their classrooms. Their first approach
is to encourage writing by using prompts, schedules and assessment rubrics
as a way for students to communicate. Topics were put on the board to get
the ball rolling for each entry. For grading purpose the entries were
measured on mathematical content and thought and expression. Journal
grades were given the same value as a test to maintain the value and
integrity. When implementing journals they give some advice, choose a
clas where they will write, decide what you want the students to write,
what the schedule is and what format they are to use. They believe that
the journals are a valuable form of assessment for both the students and
the teachers.
Keywords: Algebra, Activities,
Ref: Siverson9
Author(s): Crawford, Ann R.
Date: 2000
Title: Making Sense of Slope.
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: Vol. 93 Number 2 pg 114
Reviewer: Siverson
Date of Review: 04-19-2000
The study of variability and change is an essential algebraic concept that helps students make sense of our world through mathematics. By observing graphs and tables students learn to describe and extend patterns, create equations with variables with respect to patterns and make predictions. Hence slope and its understanding is essential for all math students.
The authors of the article want to move away from the
typical slope of a line defintion as vertical over horizontal. This has
roots that say calculation is more important than understanding. The
authors present slope from the beginning as a concept of change through
visualization from graphs and other tables, verbalization from articles
and real applicaions, and symbolism of equations and variables. In this
way understanding and critical thinking is more important than the correct
answer. I would essentially agr
Keywords: Activities, Algebra,
Ref: Siverson10
Author(s): Peterson, Blake. Averback, Patrick. Baker,
Lynanna
Date: 1998
Title: Sine Curves And Spaghetti
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: Vol 91 Number 7, pg 564
Reviewer: Siverson
Date of Review: 04-26-2000
This activity that is outlined in this article pertains to
trigonometric ratios and right triangles. It is really quite interesting.
Cooked spaghetti is used along with large rolled out sheets of paper about
3 ft by 6ft. On one side of the paper is a unit circle. The other side
is the positive x axis with y from -1 to 1. Students use spaghetti to
find the ratio between the radius and the height of the triangle for a
certain angle measure in the circle. Then the ratio is marked on the x
axis corresponding to the angle that was used. In this way students can
manipulate something that appeals to their concrete understanding, yet is
mathematically correct in the abstract sense. In the end a Sine curve
results on the x axis. The activity could be fixed so that a Cosine curve
results. This activity is a powerful and yet simple activity I believe
for making the connection bet
Keywords: Teaching Strategies, Algebra,
Ref: Siverson11
Author(s): Kreminski, Richard
Date: 1998
Title: Fun Fractions? You've got to be Kidding!
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: Vol 91 Number 7, pg 572
Reviewer: Siverson
Date of Review: 04-26-2000
This article considers the decimal expansions of some certain fractions and the interesting patterns and sequences that result in them. Like the evens sequence or odds only, sequences of squares or other things are interesting. They can be modeled in functions that are really quite combinatorial with the background that is present. It is here that the class can explore how to make fractions that give the desired sequence when in decimal expansion. The next step is to look for convergence if it exists.
This could really work and be interesting. But the
combinatorical arguments and theory that are behind the functional
expansion of the fractions may be reserved for students who understand
calculus and Taylor expansion stuff.
Keywords: Teaching Strategies, ,
Ref: Siverson12
Author(s): Masingila, Joanna O
Date: 1998
Title: Thinking Deeply about Knowing Mathematics
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: Vol 91 Number 7, pg 610
Reviewer: Siverson
Date of Review: 04-26-2000
In this article Joanna looks at trying to get new and old teachers
alike to thing more deeply about their math subjects. Most Math teachers
know a lot of math, and know that. But not always do they think that
deeply or they to consider how conceptually deep, connected or broad it
is. An important part of the professional development should be thinking
deeply about knowing mathematics. In that way teachers can reflect in two
ways 1) About what it means to know mathematics, 2) what their own
understanding of fundamental mathematical ideas are. From there teachers
are much better situated to address their class properly. Because
teaching is not the same as knowing, getting teachers to think deeply can
be enlightening and give valuable insight to instruction. Finally Joanna
says that thinking deeply about mathematical ideas and concepts "allows
teachers to develop deeper under
Keywords: Teaching Strategies, ,
Ref: Siverson13
Author(s): Kaplan, Rochelle G.
Date: 1997
Title: Teachers-Clinicians Encourage Children to think as
Mathematicians
Journal or Publisher: Teaching Children Mathematics
Volume, Issue, Pages: Volume 6 number 6 pg. 407
Reviewer: Siverson
Date of Review: 04-30-2000
To counter negative dispositions and anxiety to math, teachers must
consider
interventions that go beyond regular classroom strategies. The center for
Math Success, an after school program, gives an intervention that puts
teachers in a clinician role who sensitively uncovers misconceptions and
builds and clarifies mathematical concepts. The strategies to
interviewing students to find out information from students have one main
purpose, to listen to students and not correct them. Then in the
beginning misconceptions are identified and teachers can know which area
to build a plan to have the student relearn the concepts. The plan should
include scaffolding that provides supportive cues to help their thought
process. Through these processes young people who had not had success in
math earlier are able to turn around and succeed in math.
Keywords: Teaching Strategies, ,
Ref: Siverson14
Author(s): Schielack, Jane F. Chancellor, Dinah. Childs,
Kimberly
Date: 2000
Title: Designing Questions to Encourage Childrens
Mathematical Thinking
Journal or Publisher: Teaching Children Mathematics
Volume, Issue, Pages: Volume 6 number 6 pg. 398
Reviewer: Siverson
Date of Review: 04-30-2000
In the article is an outline about a professional development program/
session that focused on experiencing and analyzing worthwhile activities
to address the Number sense of students. They developed 3 main types of
questions that need to be asked more often while activities are being
done. The difference that questions make in activities can make a 15
activity go for sometimes 45 with exploration and questioning. The
questions are aimed at; A) Encouraging student exploration of
mathematical ideas in the activity, B) guiding the summarizing discussion
at the close of the activity, and C) assessing student learning during and
after the activity. These types of questions that need to be asked also
point directly at different modes of thought. The modes are; modeling,
abstraction, optimization, logical analysis, data analysis and symbols.
After questions using these patterns
Keywords: Activities, ,
Ref: Siverson15
Author(s): Tanton, James
Date: 1999
Title: Iterated Sharing
Journal or Publisher: Math Horizons
Volume, Issue, Pages: Page 26
Reviewer: Siverson
Date of Review: 04-30-2000
For many Mathematical Ideas numbers and equations are used. But many
mathematical things can be physical and very hands on situational
modeling. One such opportunity for a hands on approach is this Iterated
Sharing activity. A group of people begin with any number of candies
provided it is an even number. Then upon each round, everyone gives half
of their candies to the person on their right. (all at once) If someone
now has an odd number then they can draw one candy from the reserve pile
to restore them to an even count. This continues for many many rounds.
With these perimeters set up any number of hypothesizes can be tested and
conjectured. Then proofs can be created and tested in a large variety of
mathematical areas.
Keywords: Activities, Technology,
Ref: Siverson16
Author(s): Horton, Bob
Date: 2000
Title: Making Connections Between Sequences and Mathematical
Models
Journal or Publisher: Mathematics Teacher, May 2000
Volume, Issue, Pages: Volume 93 Number 5 pg 434
Reviewer: Siverson
Date of Review: 05-03-2000
The ideas of presenting Geometric and Linear models is nothing new in
secondary education. That includes Geometric and Arithmetic sequences
also. In these ideas there can be lots of notation that can confuse,
complicate and cover up the main idea behind sequences and sums. The use
of spreadsheets can mitigate the confusion with the notation and make the
desired connections. This article describes a 3 phase 5 day project that
a teacher could use in class to help model geometric, linear and
exponential growth and sequences. This type of activity also lends itself
well to a parallel journaling activity as well. The Project it quite more
extensive and detailed than I could possibly explain here, basically it
just uses an excel type set up to graph and sequence numbers and formulas.
But additionally students can find and make connections to slope,
formulas, initial values, y in
Keywords: Equity, ,
Ref: Siverson17
Author(s): Makros, Jan
Date: 1999, Jan.
Title: The Glass Wall
Journal or Publisher: The World Wide Web, Online
Volume, Issue, Pages:
http://www.terc.edu/mathequity/gw/html/papers.html
Reviewer: Siverson
Date of Review: 05-03-2000
Popular culture offers little outside-of-school support for children's
mathematical learning. Computer games are a potential exception. These
games exert a tremendous pull on some children. While many games purport
to be educational and even to promote children's mathematical learning,
there is little research to support these claims. Researchers are
beginning to get a handle on the conditions under which students learn
mathematics in school, yet almost nothing is known about how computer
game-playing can support and extend children's knowledge of mathematics.
In addition, researchers and software developers have paid little
attention to the disparities between boys' and girls' involvement with
these games. While computer games could provide the opportunity for
increased mathematical learning by both boys and girls, the reality is
that girls are not benefiting from the potentia
Keywords: Connections, ,
Ref: Siverson18
Author(s): Rock, David. Shaw, Jean M.
Date: 2000
Title: Exploring Children's Thinking About MAthematics and
Their Work
Journal or Publisher: Teaching Children MAthematics
Volume, Issue, Pages: Volume 6 number 9 page 550
Reviewer: Siverson
Date of Review: 05-10-2000
As we have learned from reports, fewer students are going into careers
that use
mathematics. Probing students thinking about mathematicians and their
contributions and roles in society fosters insights for classroom
teachers. On the basis of what students think about mathematicians,
teachers might alleviate misconceptions and broaden students thinking
about their role as a future mathematician. The authors came up with 3
questions that they asked to K-8 graders to find out what students
conceive mathematicians to be and do. 1) What do mathematicians do? 2)
What types of problems to do mathematicians solve? 3) What tools do
mathematicians use? From the answers that they received they concluded
that it was extremely important to stress that math is used in everyday
life by everyone. Then they will learn the value of math education.
Keywords: Assessment, ,
Ref: Siverson19
Author(s): Alcaro, Patricia C. Katims, Nancy
Date: 2000
Title: Fractions Attack
Journal or Publisher: Teaching Children MAthematics
Volume, Issue, Pages: Volume 6 number 9 page 562
Reviewer: Siverson
Date of Review: 05-10-2000
This article looks into how to find out if students are thinking
mathematically and what situations best show this. They explore those
questions through two videotaped sessions with students thinking and
talking mathematically while tackling a complex real life investigation.
The students were given information and introduction and then the student
groups were let loose to develop a method to solve the task. Here
hypothesis testing and prediction were involved. Through lively
discussion and teacher questions students worked together to understand
the math involved. The writers could see many different aspects to
observe the understanding of students. One was that they saw
understanding of answers but no checking to be sure. Another was that
they expressed concepts
correctly but could only express it one the one manner, there was no
transition. These indications are what teachers need to look for to
really see their student's position. Such activities can be used very
effectively to show how students are building and producing higher levels
of thought.
Keywords: Activities, ,
Ref: Siverson20
Author(s): Gale, David
Date: 1998
Title: Egyptian Rope, Japanese Paper and High School MAth
Journal or Publisher: Math Horizons
Volume, Issue, Pages: Sept 1998 pg 5
Reviewer: Siverson
Date of Review: 05-10-2000
David Gale examines the connection between the activity of paper folding and understanding of mathematical concepts. He says, "Origamics study is valuable for high school students. It develops mathematical and scientific though and provides an opportunity to use a computer with a sense of purpose." With such a simple paper folding activity as this and the recurrence of the Egyptian right triangle ratio it takes math into a new area for students. Is math like this just coincidence or is there a mathematical explanation or pattern that produces the results time and again. This step from play time to number theory and geometry is very easy and exciting for students to explore.