Keywords:
Research
Ref: Sarah1
Author(s): Kloosterman, Peter; Rutledge, Zachary; Kenney,
Patricia Ann
Year of publication : 2009
Title: Exploring Results of the NAEP: 1980s to the Present
Journal or Publisher: Mathematics Teaching in the Middle School
Volume, Issue, Pages: Vol. 14, No. 6, pgs 357-365
Reviewer: Sarah
Date of Review: February 15, 2009
This
article reviewed the outcomes
of the past three decades of the National Assessment of Educational
Progress
(NAEP). They focused mainly on the results of the 1973-2004 Long-Term
Trend
(LTT) Assessment in mathematics. Some of the items used on the test
were
released in 2006 and the authors go over the findings to see what our
schools
are lacking. They discovered that “results of the LTT assessment for
middle-grades students show[ed] positive advancement”. However, more
specifically they discovered areas that need to be addressed more in
middle
schools or that don’t need the emphasis as much as we thought.
The
final part of the article spoke
particularly to me because it spoke about how, although students have
the
ability to do the computations in word problems they aren’t as likely
to score
these points because of the more conceptual items involved in the
problem. This
leads me to believe that focusing on teaching through problem solving
would be
a good way to prepare the students for using their computation skills
in real
life examples.
Keywords:
Equity/Diversity
Ref: Sarah2
Author(s): Imm, Kara Louise; Stylianou, Despina A.; Chae, Nabin
Year of publication : 2008
Title: Student Representations at the Center: Promoting
Classroom
Equity
Journal or Publisher: Mathematics teaching in the Middle School
Volume, Issue, Pages: vol. 13, No, 8, pg.458-463
Reviewer: Sarah
Date of Review: February 22, 2009
This
article on equity talks through
an experience with a lesson taught by Kara Imm, one of the authors. She
is
trying to guide her students through as lesson on multiplying factions
by using
representation to real life situation. She speaks about how important
the
representation of mathematical ideas is to help students create a
mindset of
relevance and meaning in order for them to gain the necessary
comprehension and
skills. Although when a teacher creates their own representation of a
problem
it can sometimes be difficult to find an example that relates directly
to the
students. So because of this Imm suggests that instead of creating your
own
representations we allow the students to have a hand in creating the
examples.
This allows for a close to home representation of mathematics through a
student’s idea for math in his or her own world. Another plus of
letting
students create their own representations is that then the teacher is
able to
use these ideas to furt
her
gain insight on the background
and culture of the students in the classroom. Through this article I
was able
to see how one would implement this strategy of student representation.
She
states 3 ways of creating equity in the classroom that really suck with
me. She
states that the 3 ways are; “(a) by helping students feel that they are
a part
of the culture of mathematics, (b) by creating a mathematics community,
and (c)
by holding students accountable for their mathematical growth.” I
believe that
through implementing these three steps a teacher can create more
equality when
creating representation example through realizing that students come
from
different backgrounds so varying the examples would help them get the
mathematical ideas down through real life examples.
Keywords:
Connections, Algebra,
Ref: Sarah3
Author(s): Lee, Ji-Eun; Kim, Kyoung-Tae
Year of publication : 2008
Title: It Is a Piece of Cake: Algebraic Thinking in a
Real-Life
Situation
Journal or Publisher: Mathematics Teaching in the Middle School
Volume, Issue, Pages: Vol. 14, No. 1, August 2008
Reviewer: Sarah
Date of Review: February 24, 2009
Cake
is filled with sugar and cake a
good real life example for thinking of algebra to get the correct
amount of
cake pieces for the party people. This article takes this idea of
cutting a
cake into pieces as an algebra problem and puts it to use connecting it
to the standards
and principles of middle school mathematics. Through this activity we
can
relate the cake example to the standards of algebra, problem solving,
reasoning
and proof, connections and representations. The article speaks on how
each of
these standards relates to the sharing of a cake problem through
separate
activities.
I
believe that this is a good
article because it clearly illustrates each of the planned
lessons/activities.
The most important part about each of the activities in the article is
that it
allows different ways to explore the problem of cutting the cake
through the
separate standards and principles. This is a good article to create a
couple
days focusing on this one problem of cutting the cake. I would use it
to help
teach students about how there are different ways to look at a problem
and
there are different conclusions. Plus it can become a great snack on
the last
day of the unit activity.
Keywords:
Representations, Algebra
Ref: Sarah4
Author(s): Hyde, Arthur; George, Katie; Mynard, Suzanne; Hull,
Christina; Watson, Sharon; Watson, Patrick.
Year of publication : 2006
Title: Creating Multiple Representations in Algebra: All
Chocolate,
No Change
Journal or Publisher: Mathematics Teaching in the Middle School
Volume, Issue, Pages: Vol. 11, No. 6 pg.262-268
Reviewer: Sarah
Date of Review: March 1, 2009
The
goal is to make algebra more
accessible to students and in order to do that we need to have enticing
mathematics for students to gravitate towards in the classroom. The
more
traditional way of teacher algebra by tackling an equation without
context,
making a table, and graphing isn’t working. The authors suggest
starting at
concrete representations and then move to increasingly more abstract
problems
of the same concept. The most powerful of understandings occurs when
students
can come to recognize the connections between the learned
representations. For
the authors specific beginning problem to algebra they introduced a
situation
for students to find the different ways $10 could be used to buy two
different
priced candies. Students could then progress from being able to “build
a strong
base for representing real-world situations with tables and graphs, to
introduce linear equations, and to bridge linear equations and systems
of
equations.”
This
article gives a well-detailed
approach to helping connect students with the algebra. I would use this
grouping of activities to create a foundation for algebra for my
pre-algebra
students. The lesson walks you through the different ways to see the
problem
and also creates options for you to take the more experienced students
further
into their learning of the subject and modifications for younger and
special
needs students. This article has a good set up so that you may easily
differentiate the different intensities and learning style of several
different
groups of students within he same classroom.
Keywords:
Communications, Geometry
Ref: Sarah5
Author(s): Robichaux, Rebecca R.; Rodrigue, Paulette R.
Year of publication : 2003
Title: Using Origami to Promote Geometric Communication
Journal or Publisher: Mathematics Teaching in the Middle School
Volume, Issue, Pages: Vol. 9, No. 4 222-229
Reviewer: Sarah
Date of Review: March 3, 2009
This
article uses origami to teach
students geometry, developing their knowledge of spatial sense,
properties of
shapes, congruence, similarity and symmetry. It also shows students
about the
multicultural connections in math and deals mostly with the concept of
communication in the classroom. It is important for all students to
communicate
their own mathematical thinking to their peers and teachers. Using
words to
express mathematical ideas and problems can be difficult for students
who have
never been asked to do so before. It is imperative to remember that as
teacher
we need to facilitate this discussion within the math classroom.
Research has
shown that when students know how to express themselves mathematically
it
increases their understanding of the concepts and ideas. “Mathematics
becomes
personal through oral communication”(223).
The
lesson described in this article
is planned to take two 50-minute periods. As an overview the lesson
uses
“cooperative group learning, peer teaching, journal writing, and a
hands-on
approach to teach geometric concepts”(224). I am especially attracted
to the
part of the lesson when they are actually doing the folding of the
origami.
Instead of just handing out instruction for how to fold the paper a
question
guide accompanies the students and asks questions after each fold. Each
question brings the origami lesson to a new level of learning through
communication
between the students at the group tables. It forces the students to
actually
think about how the paper is being folded. The questions relate back to
the
main concepts of geometry; shape, area, and fractions of shapes. The
second
part of the lesson has the students teach their partners about how to
make the
model that they had perfected. Once again, there are question that
follow after
each has taught their neighbor, forcing the students to think and
explain how
they communicated the origami.
I
especially enjoyed this article.
It is full of ideas to help generate communication of mathematics
within the
classroom. By allowing students to become the teachers it lets them
dive deeper
into their schoolwork. All the activities in the article meet the
Geometry
Standard of NCTM. The article also has further extensions that a
teacher could
pursue to help the students explore the origami even further. If I was
teaching
a geometry lesson I would want to use this plan to help my students
understand
how to communicate the mathematics that they were doing.
Keywords:
Number and Operation
Ref: Sarah6
Author(s): Bay-Williams, Jennifer M.; Martinie, Sherri L.
Year of publication : 2003
Title: Thinking Rationally about Number and Operations in
the Middle
School
Journal or Publisher: Mathematics Teaching in the Middle School
Volume, Issue, Pages: Vol. 8, No. 6, pg. 282-287
Reviewer: Sarah
Date of Review: March 8, 2009
The
article use of three scenarios
shows us the idea of relative size of fractions, fraction computations
and
proportional reasoning illustrating some of the standards of middle
school
math. The authors describe classroom experiences with the previous
problems to
understand rational numbers. They found that when students are asked to
“determine the larger of two fractions or two decimals, they often do
not have
a sense of the size of that value when it is related to 0, ½,
and 1”(282).
They
introduced the game of “red
light, green light” to help describe the fractions from the distance to
the
start and finish line. They found that some students would rely on
their
understanding of decimals and convert the fractions in order to find
the
position on the number line. Some students used rulers to find the
fractions.
The article talks about the different ways students used to find the
fractions
of the distance of the players. They found that some students used
“flexi!
bility with numbers include[ing] (1) working flexibly within a form
(i.e.,
among fractions only); (2) moving among fractions, decimals, and
percents; and
(3) knowing which form is most useful, given the problem at hand”(284).
Further
into the lesson we develop which of these forms is most useful
according to
different situations. Additional problems were given to the students to
help
them see these differences. They need a lot of experiences to guide
them to
develop their understanding of problem solving and examples were given
to guide
them to different forms.
Lastly
the article talked about how
it incorporates the meanings and use of mathematical operations and
proportionality into the context. By focusing on the understanding of
the
operations students can apply their knowledge to help create algorithms
for
shifting from whole numbers to fractions. By allowing the students to
experiment with their own algorithms it allows them to make sense in
their own
way about the rule to “multiply by the reciprocal” for fractions. This
article
gave a good overview of some ideas to help middle school students use
fractions
in context to help intrigue the students and engage them in the
learning that
is taking place in the classroom. It is important to start students to
think
with a rational mind in order to start a successful path toward
algebra.
The
article builds an activity that can be used to help students understand
the
idea of variation from the mean. By developing concepts like
distribution of
data, variation in data and the use of MAD as a measurement of
variation in the
data students are introduced into the main concepts of statistics. The
activity
is surrounded around a problem of how many people are in the students’
families. By using sticky notes the students created a line plot
displaying the
data of family size for 9 families that had a mean of 5. They students
had to
rely on their knowledge of how to calculate the mean in order to create
a
distribution on the number line that corresponded to a mean of 5. After
each
group of students had created a different number line with their sticky
notes
they were asked to compare the different plots all with mean 5. It
became
prevalent that although knowing the mean can give us information about
the
total population it doesn’t provide us with enough information to talk
about
the distribution of the data.
Taking
the activity to its main goal the teacher then helped walk the students
through
describing the different distributions in each of the plots that had
been made,
finally coming to the definition of deviation from the mean as
value-mean.
Recognizing that there is a difference in the deviation of each of the
plots is
important to understand that each plot illustrates a different idea.
The second
part of the lesson demonstrates for the students the definition of MAD
(mean
absolute deviation) and how to implicate it in each of the example data
sets.
Furthermore the teacher not only develops and understanding of how to
find the
MAD but also how to comprehend it within the context.
I
find this article to be a good framework for a lesson surrounding
statistics
and mean however I’m still a little bit confused about the idea of MAD.
I had
never heard that term before and am interested in if this is still used
today.
The overall approach to an introduction to deviation works well within
an
engaged classroom and would be appropriate to use to help develop
students’
further understanding of how to read and analyze data.
Keywords:
Connections, Probability, Statistics
Ref: Sarah8
Author(s): Colgan, Mark D.
Year of publication : 2006
Title: March Math Madness: The Mathematics of the NCAA
Basketball
Tournament
Journal or Publisher: Mathematics Teaching in the Middle School
Volume, Issue, Pages: Vol, 11, Nov. 7 pages 334-342
Reviewer: Sarah
Date of Review: March 15, 2009
This
article uses mathematics involved in the NCAA basketball tournament to
begin or
review a unit on probability and statistics. The author suggests doing
the unit
before or after spring break in order to help motivate the students
during that
difficult time when spirits and minds are outside of the classroom and
focused
on spring.
The
article begins by talking about the tournament terminology for people
like
myself who know nothing about the NCAA tournament. The tournament is
called
“March Madness” and the first round has 64 teams with 32 winners, then
leading
into the “Sweet Sixteen”, then 8, then 4, then the final two resulting
in a
winner. Some of the math used to figure out the strength of schedule is
to use
the rating percentage index (RPI). The committee uses the RPI to figure
out
what teams should be placed where in the tournament. The article talks
about
the history of the seeds and how to compute the RPI for a team.
The
second part of the lesson talks about probability and figuring out the
possibilities that certain seeds will win certain games. Then leads
into the
idea of expected value as an event of average for figuring out the long
run
events and multiplication principle. The author begins each of the
sections
with examples of the ideas with connections to easier problems before
introducing the harder basketball connections. The article also
includes a
great exercise to review the material learned. It also recommends an
additional
project that can create some competition between the students giving
them a
chance to try and use the math to pick the final four teams for the
men’s and
women’s tournaments. Over all a very worthwhile article especially if
there are
a lot of students who are real big fans of basketball and the
tournament.
Keywords:
Algebra, Teaching Strategies, Activities
Ref: Sarah9
Author(s): Menon, Ramakishnan
Year of publication : 2004
Title: Motivating Activities That Lead to Algebra
Journal or Publisher: Mathematics Teaching in the Middle School
Volume, Issue, Pages: Vol. 98, No. 1 pg. 26-31
Reviewer: Sarah
Date of Review: March 17, 2009
The
article helps teachers make
algebra interesting for students. There are many students believe that
they
can’t do algebra because they believe it to be a lot of “symbol
manipulations”
and solving complicated equations. The author describes several
activities that
he has used in the past to get students involved in their learning of
algebra.
He uses “puzzles and patterns that lead to algebraic generalizations”
to help
students see the ideas and create their own problems.
The
first activity is called the
constant-sum grid. This activity uses a 4-by-4 grid filled with
numbers. Then
by following 9 steps and adding up the sum of the circled numbers it
will
always be 45. The teacher will guide the students through the activity
and
encourage them to look for patterns and help figure out why they always
have
the same sum even though different sets of numbers are circled. There
are good
follow up questions that allow students to explore the idea further to
develop
a better understanding of the algebraic pattern.
The
second activity is an
exploration of the Fibonacci sequence. By creating their own Fibonacci
sequence
students figure the pattern through exploration and some algebraic
guidance.
The third is called predict your age uses an algorithm to set up an
answer to a
person’s age and number of people in their family. It seems like mind
reading
until students have the ability to see the algebraic steps that were
taken to
get to the answer. The final activity is called target 21. This games
also
involves 2 students choosing a number 1, 2, or 3 to add on to the
previous
total switching turns and starting at 0, the first student to reach to
21 wins.
The students will look backwards to figure out how to always win the
game by
finding safe numbers.
All
this activities help students
come to understand the importance of algebra when it is used to
generalize
situations by creating a game/activity students are more likely to be
engaged
and motivated to find solutions. These can be starting points to
introduce
students to formulate a general arithmetic sequence. The activities are
described in good detail and could be used in a classroom setting. They
are
interesting, help students develop an algebraic way of thinking and let
students create new problems and puzzles of their own. Over all this
would be
an excellent article to read and implement if introducing students to
algebra
through games and activities.
Keywords:
Equity/Diversity, Geometry.
Ref: Sarah10
Author(s): Murrey, Deandrea L.
Year of publication : 2008
Title: Differentiating Instruction In Mathematics for the
English
Language Learner
Journal or Publisher: Mathematics Teaching in the Middle School
Volume, Issue, Pages: Vol. 14, No. 3, pg. 146-153
Reviewer: Sarah
Date of Review: April 1, 2009
With
around 5 million students
considered ELLs it is important to further education for teachers about
how to
best reach these students. The four principles that are used to develop
language acquisition are (1) comprehensible input, (2) contextualized
instruction, (3) a low-anxiety learning environment, and (4) meaningful
engagement in learning activities. The article walks through these four
principles and offers suggestions to how they can be used within the
mathematics classroom. There is a very complete table, which summarizes
these
principles and adds specific strategies that can be used to help teach
the
principle.
The
second part of the article walks
through investigating the perimeter and area of objects through
problem-solving
techniques. By participating in the development of the formulas
students will
gather a better understanding for the definition and use of the
formula.
Through investigations the article walks through engaging activities
that will
further a students understanding of area and perimeter. Through these
investigations they are required to use the principles above to explain
the
activities. The careful exploration of the shapes is enhanced through
the
language proficiency that is being acquired through the problem-solving
activities.
I
would highly recommend reading
this article mainly for the table that organizes the language
acquisition
principles and strategies. If one is ever working in a classroom with
ELL
students it is important to remember that there are many useful
recourses out
there that can be of much use when trying to create lesson plans that
are
helpful to create language proficiency while still teaching
mathematics.
Keywords:
Technology
Ref: Sarah11
Author(s): McGehee, Jean; Griffith, Linda K.
Year of publication : 2004
Title: Technology Enhances Student Learning across the
Curriculum
Journal or Publisher: Mathematics Teaching in the Middle School
Volume, Issue, Pages: Vol. 9, No. 6, Page 344
Reviewer: Sarah
Date of Review: April 5, 2009
The
main point to always keep in
mind is that technology does not replace the need to teach basic
understandings
and skills. As teachers we need to learn how to use the technology as
an
additional manipulative to help the students understand in an
supplementary
way. The article walks through the different content stands of
mathematics;
data analysis and probability, algebra, number and operations,
geometry, and
measurement. Each sections speaks on a separate content stands giving
specific
activities that can be used with technology along with the program
(particular
technology) that can help do this.
The
five examples implement the use
of the calculator, spreadsheets, geometric software, and a CBR that
tracks
movement. Each of the examples would prove to be much more time
consuming and
difficult with the absence of the necessary technological tools.
Although the
sections speaking on the stands are very short I believe this is a good
jump-start towards implementing technology in the classroom across all
the
stands presented as examples.
Keywords:
Problem Solving, Connections, Representations
Ref: Sarah12
Author(s): Santulli, Tom
Year of publication : 2009
Title: Representations from the Real World
Journal or Publisher: Mathematics Teaching in the Middle School
Volume, Issue, Pages: Vol. 14, No. 8, Pg 466
Reviewer: Sarah
Date of Review: April 19, 2009
Tom
Santulli believes that
“providing a real-world context and requiring multiple representations
will
promote students’ understanding of problems.” It is important to have
many
levels of representations to allow for students to understand how to
use the
tools properly. Santulli believes that it is critical for middle school
math to
teach students the necessary representations in order to succeed in
high-level
high school mathematics. It is key to help students recognize that
problems can
be represented in several forms as to help their overall comprehension
of the
problem. It is the job of the teacher to help take the students from
the
elementary understanding of representation from grade school into a
more advanced
comprehension that will allow for them to be successful problem
solvers.
The
article walks us through 4
problems using the themes of car rentals, boxes, movie tickets and dog
grooming. The 4 problems show different representations for the
problem.
Through a successful use of all 3 representations for problem 1, the
dog-grooming problem, will make the high mathematics more accessible to
the
students. By making a table to represent the problem then move on to a
functional equation then a graphical representation allows for easy
access of
the mathematics for the students. The next problems trail as more
challenging
follow-ups to the idea of representations and problem solving. Each
detailed
enough to implement within the classroom as a successful problem
solving
representation lesson. By helping students understand multiple
representations
we are allowing for them to reach higher levels in mathematical
understanding.
Keywords:
Teaching Strategies, Standards
Ref: Sarah13
Author(s): Brucker, Elizabeth L.
Year of publication : 2008
Title: Journey into a Standards-Based Mathematics Classroom
Journal or Publisher: Mathematics Teaching in the Middle School
Volume, Issue, Pages: Vol. 14, No. 5, Page 300-
Reviewer: Sarah
Date of Review: April 19, 2009
“A
standards-based approach in
mathematics involves using story problems to allow students to
investigate a
solution. This approach emphasizes an understanding of concepts and
processes
and assumes mastery of basic computation skills.” The new NCTM goals
are to
help students and teachers change their thinking of mathematics. The
article
speaks on Elizabeth Brucker’s journey towards a belief in
standard-based
teaching. Brucker struggled in mathematics as an elementary student and
when
she began her career as an elementary school teacher she carried that
discomfort with her. She would avoid the word problems in the books as
she saw
them as extremely challenging. She realized that these problems were
the best
parts of the lesson by teaching students to think. The rest of the
article she
talks about her journey to becoming a better math teacher as her love
for math
grew. She concludes saying that it is important for teachers to have
training
to be able to teach standard-based mathematics correctly and
effectively.
Keywords:
Algebra, Teaching Strategies
Ref: Sarah14
Author(s): Usiskin, Zalman
Year of publication :
Title: Conceptions of School Algebra and Uses of Variables
Journal or Publisher: The Ideas of Algebra, K-12
Volume, Issue, Pages:
Reviewer: Sarah
Date of Review: April 19, 2009
“School
algebra has to do with the
understanding of “letters” and their operations.” This school algebra
is so
different from the mathematics of algebra taught in college.
Considering the
following equation of two numbers equaling a third and their use of
variables:
1.
A=LW
2.
40=5x
3.
sinx=cosx X tanx
4.
1=nX(1/n)
5.
y=kx
Each
of these has a specific
definition within algebra (1) a formula, (2) an equation to solve, (3)
an
identity, (4) a property, and (5) an equation of a function. Today the
idea of
a variable is the “symbol for an element of a replacement set”.
The
two fundamental issues in
algebra are the requirement to be able to do various manipulative
skills by
hand and the question of the role of functions and the timing of their
introduction. There are four conceptions presented in this article;
algebra as
generalized arithmetic (pattern generalizers), as a study of procedures
solving
certain kinds of problems (unknowns and constants), as the study of
relationships among quantities(arguments, parameters) and as the study
of
structures(arbitrary marks on paper).
Keywords:
Geometry, Teaching Strategies
Ref: Sarah15
Author(s): Bell, Clare V.
Year of publication : 2003
Title: Learning Geometric Concepts through Ceramic Tile
Design
Journal or Publisher: Mathematics Teaching in the Middle School
Volume, Issue, Pages: Vol. 9, No. 3, page 134
Reviewer: Sarah
Date of Review: April 19, 2009
Examples
of cultural geometric art
are used to teach a lesson in symmetry and geometric patterns. This
article
goes through several lessons designed to help students learn about
two-dimensional geometry by creating their own ceramic tiles. Through
the
exploration of lines, angles, circles, triangles, quadrilaterals, and
regular
and nonregular polygons the students gather properties in order to
create their
own tile. As they are going through the lessons they “develop more
precise
descriptions and classifications, thus increasing their ability to
create and
critique inductive and deductive arguments concerning geometric ideas
and
relationships.”
Lesson
1 explores regular polygons
to start scaffolding up towards the larger concepts. The second lesson
delves
into the concepts of construction of a regular hexagon. Lesson 3 goes
into the
examinations of the art of cultures and then in lesson 4 has students
recreate
the designs from the previous lesson. Each lesson builds on the
previous
guiding the students towards creating a beautiful geometric design for
their
tiles.
This
research project analyses the problem solving skills based on reading
comprehension. There were 98 sixth and seventh graders who participated
by
having their problem-solving behaviors classified into five categories.
They
found that to succeed in solving word problems students must be able to
transform elements of the word problem into a whole conceptual idea.
The
“findings of this study suggest several potentially crucial components
[by]
translating the text of a word problem, constructing an accurate mental
model,
and solving mathematics word problems”(208).
Some
important characteristics found in the research included;
-student
recorded the information of the problem
-student
used in context with units and associations and to support conclusion
-the
more successful students showed evidence that they translated and
organized the
information by rewriting
There
are five main categories;
Direct
Translation Approach (DTA)-not proficient-lack of competence and have
difficulty reading the problem, coming to an understanding of the
problem,
deciding on a solution, performing calculations, students also are
hesitant in
moving towards a solution. They reread the problem and some calculation
may not
even be related to the problem.
DTA-proficient-
Students can automatically and efficiently translate elements of the
problem
into a mathematical computation with only one reading.
DTA-limited
context-they can translate the elements of the problem to arithmetic
computation but with limited context.
Meaning-Based
Approach (MBA)-full context-Students read and reread the sentences of
the
problem and record the information in the correct context and use this
to
support calculations. The final answer is given in a complete sentence.
MBA-justification-
is similar to the previous classification but in addition student have
evidence/justification for each step.
Keywords:
Problem Solving, Teaching Strategies
Ref: Sarah17
Author(s): Edited By: O'Daffer, Phares G.
Year of publication : 1988
Title: Selections from Arithmetic Teacher
Journal or Publisher: Problem Solving: Tips for Teachers
Volume, Issue, Pages:
Reviewer: Sarah
Date of Review: April 26, 2009
There
are many great tips for
teachers to use for teaching problem solving. Each article has several
different sections. They begin with a Strategy Spotlight-the main
problem,
Classroom Climate (talks about different techniques for working in the
classroom), Problem Corner, Developing Problem-solving Skills, tips
from
readers, try this, background ideas, take a look, and give it a try.
Each of
the sections helps work through the problem-solving articles through
their own
tips and techniques. There are a couple of techniques that I felt were
good and
should be mentioned in my review.
The
four top method-
1.
Read the problem (important
information, visualize the situation, restate the problem)
2.
Diagram or represent the problem
(is the data correct, what conclusions can you draw)
3.
Set up the calculations and
compute (computations correct, all important data included and
organized).
4.
Write the answer (does the answer
make sense, can you check it).
To
help motivate students and their
interest in the problem solving. Personalize the problem to meet the
students’
interests. Use some students’ problems by having them write their own.
Use
interesting data for example world records or polls.
These
articles work well to help
teachers work through different ways to work through problem solving in
their
classroom. It is organized well and would be easy to implement in the
classroom.
Keywords:
Algebra, Teaching Strategies
Ref: Sarah18
Author(s): Wygant, Sue
Year of publication : 2009
Title: Developing Algebraic Thinking in Grades 6-8
Journal or Publisher: MCTM Spring Conference Duluth
Volume, Issue, Pages: Workshop Friday 8:40-10:10 AM
Reviewer: Sarah
Date of Review: May 3, 2009
This
workshop at the MCTM conference
discussed research that had been done to help explain algebraic
thinking in
elementary students and how that translates into middle school
algebraic
thinking. The speaker helped us see that we are disconnected from the
equations
as we solve for the “correct” answer and she believes that as teachers
we need
to reconnect students to their own thinking (meta-cognition). Sue
Wygant spoke
on how we need to focus on three main factors when teaching algebra;
the
underlying ideas, student work, and where the learning is going next.
In
addition she defined mathematical
proficiency by 5 separate strands; conceptual understanding, procedural
fluency, strategic competence, adaptive reasoning, and productive
disposition.
These strands all need to be covered in depth in order to ensure that
students
will achieve the algebraic thinking necessary. As a conclusion she
stated that
for kids to learn mathematics as teachers we need to engage student’s
preconceptions, acknowledge that understanding requires factual
knowledge and
conceptual procedures, and a meta-cognition approach enables students
to self
motivate.
Keywords:
Geometry, Activities, Standards
Ref: Sarah19
Author(s): Geddes, Dorothy
Year of publication : 1992
Title: Geometry in the Middle Grades
Journal or Publisher: Curriculum and Evaluation Standards for
School
Mathematics; Addenda Series NCTM
Volume, Issue, Pages:
Reviewer: Sarah
Date of Review: May 3, 2009
The
Addenda Series books are set up
in a way that is extremely assessable. It is divided up between
clusters
relating to different themes within each subject. I looked at a cluster
focusing on transformation geometry. There were 5 activities that
ranged from
ideas such as transformations in a coordinate system to exploring
symmetry with
computer software. Included in the introduction to each cluster there
is a set
of objectives directly relating to the cluster. The introduction then
goes
through each activity with the materials needed and teaching notes on
each.
Following the introduction are the activity work sheets that are
helping
students reach the objectives previously stated in the cluster. Over
all this
book works wells to organize and supply specific activities that can be
used to
add more material into curriculum that maybe lacking in activities.
Keywords:
Geometry, Activities, Standards
Ref: Sarah20
Author(s): Pugalee, David K.; Frykholm, Jeffrey; Johnson, Art;
Slovin,
Hannah; Malloy, Carol; Preston, Ron;
Year of publication : 2002
Title: Navigating through Geometry in Grades 6-8
Journal or Publisher: Principles and Standards for School
MAthematics
Navigations Series
Volume, Issue, Pages: National Council of Teachers of
Mathematics
Reviewer: Sarah
Date of Review: May 3, 2009
The
Navigation series book go
through the NCTM standards and organizes them into activities to follow
these
standards. Once again I looked at the ideas focused on transformations
and
symmetry in geometry. In the introduction it speaks on the importance
of these
specific mathematical ideas and through the individual standards
indicated by
NCTM. The second part of the introduction to the chapter talks about
“what
might students already know about these ideas?”
After
the introduction to the topic
of the chapter the activities are presented. Each activity is organized
in the
following manner. First with the goals directly relating to the
standards, then
a list of the materials needed for the activity, the main instruction
of the
activity and discussion after the activity. I believe that these are
important
books to acquire throughout teaching to help develop a rich collection
of
activities that can be used to supplement the curriculum.