Keywords: Curriculum
Ref: Monica1
Author(s): Hoffman, Ellen; Caniglia, Joanne
Year of publication : 2009
Title: In Their Own Words: Good Mathematics Teachers in the
Era of NCLB
Journal or Publisher: Mathematics Teaching
Volume, Issue, Pages: Vol. 102, No. 6, February 2009
Reviewer: Monica
Date of Review: February 17, 2009
This article talks about the affect of No Child Left Behind on teachers and how it affects the students. The talked about how NCLB has many teachers teaching for the test. They then talk to a Presidential award winning teacher who feels that NCLB does not let her teach in the way that got her to win the award. Another teacher gave their advice as well saying that Education cannot be created by legislation.
This article also talks about how teachers can learn from each
other and other ways to improve teachers.
Keywords: Equity/Diversity
Ref: Monica2
Author(s): McCoy, Leah P.
Year of publication : 2008
Title: Proverty: Teaching Mathematics and Social Justice
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: Vol. 101, No. 6, Febraury 2008, 456-460
Reviewer: Monica
Date of Review: February 22, 2009
According to the National Council of Teachers of Mathematics, one goal of the mathematics instruction is connecting mathematics to real-life applications, and that is how this article came about. This article talks about how to relate a topic that many of the students are familiar and have them learn mathematics from it. The article gave different activities that relate to poverty which are good activities for math and social consiousness.
The activities she talked about were related to families under the
poverty line. There was a chart that told how much a family in poverty
makes and the students were to make a budget with this money including
all the necessities. Then the students could think about extras and see
if the families could afford it. Another activity gave data about the
percent of certain groups under the poverty line. This activity gives
the student a great opportunity to read data and make conclusions from
it. They also can make graphs from this activity. At the end they get
to reflect on how these activities relate to them.
Keywords: Connections.
Ref: Monica3
Author(s): Gay, A. Susan
Year of publication : 2008
Title: Helping Teachers Connect Vocabulary and Conceptual
Understanding
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: Vol. 102 No.3, 218-223, October 2008
Reviewer: Monica
Date of Review: February 24, 2009
This article talked about the importance of vocabulary in understanding concepts of math. The article gave examples of ways to help get students to make connections from the vocabulary word to the concept. In the beginning of the article the author gave an example of a student teacher given instructions to the students using wrong vocabulary. The students understood and knew what she was telling them to do, but the difference between the vocabulary was very important and situations like those can confuse students.
They article
gave other exercises that could be used in understanding vocabulary,
like giving examples and non examples of a definition and having the
students come up with the definition. This helps the students not only
understand what is means and what belongs with is, but also what
doesn't.
Keywords:
Representations.
Ref: Monica4
Author(s): Rubel, Laurie H.; Zolkower, Betina A.
Year of publication : 2008
Title: On Blocks, Staris, and Beyond
Journal or Publisher: Mathematic Teachers
Volume, Issue, Pages: Vol.101, No. 5, 340-344, December 2008
Reviewer: Monica
Date of Review: February 21, 2009
This article was
about a task that a group of teachers had to complete. They were given
two different problems to choose room, but in the end they came out to
have the same result. The groups worked together for about forty
minutes to come up with there solutions. The instructor then picked
groups to present there ways of coming up with the solution. He picked
in a specific order as well. The groups had different ways of doing the
problems. What was interesting is that both problem had a group who
used the same method of finding the solution, and came up with the same
answer, but there were two different problems. This article shows that
how something is presented can determine if a person will fill
successful doing it. That is why there were to different problems. Some
felt overwhelmed just by looking at the other one. This article also
shows how people can present the same thing in different ways.
Keywords: Representations
Ref: Monica5
Author(s): Rider, Robin
Year of publication : 2007
Title: Shifting from Traditional to Nontraditional Teaching
Practices Using Multiple Representations
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: Vol. 100, No. 7, 494-500, March 2007
Reviewer: Monica
Date of Review: March 2, 2009
This article talked about using multiple representations of mathematical concepts to promote connections among algebraic, tabular, and graphical representation. The author talked about their experience of teaching and how they thought they were doing a good job of representing this topic in different ways. Then they realized that when they asked a question in a different way the students were not able to answer. She notices that she had a bias for symbolic representation and even though she taught different ways, during majority of the assessments, she only asked in the symbolic way so when the students where asked the same question in a form of a graph or table they did not know the answer. She also talked about how some students would just say just teach us one way, we don't care about the rest. It is important to know the different ways because one way might be easier or better than the others.
The author also gave a good metaphor to why it is important to
learn different ways of representations. It's like if you are in an
unknown city, instrumental understanding, which the author says is like
procedure learning, will give you a route from A to B, and even if it
is not always the best route it is the only one you know that will get
you where you want to go. However, on the other hand there is
relational understanding which the other compares to conceptual
understanding. With this, you explore the town and learn different
places and be familiar with the surrounding. Now you don't just know
from one place to another, you know from any place to another. You have
build your own cognitive map. That is what we want are students to do.
We have to teach them different representation so they can build their
own cognitive map.
Keywords: Proof
Ref: Monica6
Author(s): Perrin, John Robert
Year of publication : 2009
Title: Developing Reasoning Through Proof in High School
Calculus
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: Vol. 102, No. 5, 341-349, January 2009
Reviewer: Monica
Date of Review: March 2, 2009
The article was about the importance of using proofs to understand
math. The author gave and example related to science. Like observations
are important in science, logical reasoning is important in math. If a
student is not ale to reason, then they are only able to do procedures
and examples without thought. The author than talks about how many
students don't like proof courses or don't do well in them in secondary
education because they have not had much exposure except in geometry.
He believes that the student should be doing some form of proof before
geometry and more than just in that. Many teachers don't teach it
because it is not something that is required to be tested on at a state
or national level. He then gives us examples in his Calculus classroom
of when he used proofs to help the students understand some topic
better.
Keywords: Communications, Assessment
Ref: Monica7
Author(s): Vazquez, Lorna Thomas
Year of publication : 2008
Title: A,E,I,O,U and Always Y A Simple Technique for
improving Communication and Assessment in the Mathematic Classroom
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: Vol. 102, No. 1, 16-23, August 2008
Reviewer: Monica
Date of Review: March 4, 2009
This article was about a technique titled A,E,I,O,U. This is a great way of getting students to organize their thinking process so they can communicate better and also have a better understanding of the material. This process does not just worry about the correct answer, but what got you to the answer. Sometime students may know the correct answer but have know idea how to explain how to get the answer, so by using this process, the students are able to communicate mathematically about exactly what they were doing.
The letters stand for:
When a student does this process, it is easier for them to
communicate what they have done, and it is a way of assessment, not to
just see that they can come up with the answer, but they know why and
how.
Keywords: Number and Operation
Ref: Monica8
Author(s): Davis, Brent
Year of publication : 2008
Title: Is 1 a Prime Number? Developing Teacher Knowledge
Through Concepts Study
Journal or Publisher: Mathematics Teaching in the Middle School
Volume, Issue, Pages: Vol.14, No.2, 86-91, Sept. 2008
Reviewer: Monica
Date of Review: March 15, 2009
This article was about if 1 is a prime number. The article starts to talk about the multiplication property and what it is really saying. It gets in detail how multiplication changes a little depending on the level. So a group of teachers got together and discussed this topic. They decided to look up the definition of multiplication in the dictionary and found out that in the definition it had the word "initially" which implies that the definition was not complete. Then they started talking about how we are always taught as multiplication as a closed concept when it might be better to leave the definition open ended. So a good thing to think about when using multiplication is these four phrases (which can then be completed). If multiplication is..... A factor is.... A product is... Division is....
They came to the conclusion that 1 could be prime and not prime. if
you think of it as the folding method, it is not prime because it is
the starter, but if you think of it in a dimension, there is only one
way to make it, and that is a 1x1, so it is prime. another reason why
some argue that one is not prime is because if it is, the no other
whole number do not have unique prime factorizations, like 15. 15 can
be 3x5, 1x3x5, 1x1x3x5, and so forth.
Ref: Monica9
Author(s): Gratzer, William; Carpenter, James E
Year of publication : 2008-2009
Title: The Histogram-Area Connection
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: Vol.102, No. 5, 336-340,
Dec.2008/Jan.2009
Reviewer: Monica
Date of Review: March 16, 2009
This article started of by given their definition of what statistics is. They say statistics is a collection and analysis of data, and it is used to collect, organize, summarize, interpret, and draw conclusions from data. They then talked about how graphical displays must be accurately represent reality. Later they discussed histograms and what they are used for. A problem that comes with histogram is when we information is divided in unequal intervals. When this happens if your graph is not right, the information will be read wrong. So in these situations we need to use density graphs. Then they showed how a histogram could be missed read and different ways of making your density histogram so it is not misread.
Keywords: Number and Operation
Ref: Monica10
Author(s): Rapke, Tina
Year of publication : 2008-2009
Title: Thoughts on Why (-1)(-1)=+1 Do two wrongs make a
right? Using the distributive property avoids pseudoreasoning.
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: Vol. 102, No.5, 374-376, December
2008/January 2009
Reviewer: Monica
Date of Review: March 16, 2009
This article is about how do we get our students to see that (-1)(-1) really equals +1 without using patterns or pseudoreasoning, because these methods are not always the best way. she says that resources and pseudoreasoning won't always work because they lack the sense of consistency and structure of students' number systems and the use false logic and rule makings instead. Patterns won't always work because patterns work sometimes, but not always. Like we can show that anything raised to the zero power is 1, but what happens when we raise zero to the zero power. When we use are pattern we get 1, but the real answer is undefined, so our pattern does not work here. So the way to think about why this works is through the distributive property. Then they showed a way this can be done.
Keywords: Algebra
Ref: Monica11
Author(s): Menon, Ramakrishnan
Year of publication : 2004
Title: Motivating Activities That Lead to Algebra
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: Vol. 98 No.1, 26-31, August 2004
Reviewer: Monica
Date of Review: March 30, 2009
This was a great article with really good ideas. The author talked
about ideas the use to help students take an interest in Algebra and
not just think of it as symbol manipulation, and Solving complicated
equations, and simplifying algebraic expressions. They gave three
activities that are fun for the students. One is a mind reading
activity where they explore matrices and following directions. In the
end they can see how algebra has patterns that can find great ways to
do different activities
Keywords: Gifted
Ref: Monica12
Author(s): Chval, Kathryn B; Davis, Jane A.
Year of publication : 2008
Title: The Gifted Student
Journal or Publisher: Mathematics Teaching in the Middle School
Volume, Issue, Pages: Vol.14, No.5, 267-275,December
2008/January 2009
Reviewer: Monica
Date of Review: April 12, 2009
Keywords: Technology
Ref: Monica13
Author(s): Ebras, A. Kursat; Ledford, Sarah D; Orrill, Chandra
Hawley; polly, Drew
Year of publication : 2005
Title: Promoting Problem Solving across Geometry and Algebra
by using Technology
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: Vol. 98, No. 9, 599-603, May 2005
Reviewer: Monica
Date of Review: April 12, 2009
This article was about how technology is a good device for teaching problem solving because it is a good way of showing multiple representations. They gave an example of a problem where a student will want to find the distance that two people traveled if there was a rectangular field ABCD and one person traveled AB to BC while the other traveled AC, and the differences between the two's distance must be 40 yards. One way the students might want to attack this problem is by using Geometry Sketch Pad. With this program the students are able to construct the rectangle and move points around to find out different solutions to this problem. While doing this they will be able to find that there are many solutions to this problem. So GSP gave the students a visual way to represent this problem. Another way the students can attack this problem is with a spreadsheet. Using the spreadsheet, again they will realize that there are many solutions to this problem.
This article basically showed a good way of how technology could be
used as a way for students to solve a problem in multiple ways. The
authors said that technology does not replace mathematical skills, but
it allows mathematical thinking to be accessible to all students no
matter what thinking level they are at. They also say that it is
important for the teacher to ask higher level questions and to guide
the students as well.
Keywords: Probability
Ref: Monica14
Author(s): Lanier, Susie; Barrs, Sharon
Year of publication : 2003
Title: Lets Play Plinko: A lesson in Simulations and
Experimental Probabilities
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: Vol. 96, No.9, 626-629, December 2003
Reviewer: Monica
Date of Review: April 12, 2009
Keywords: Equity/Diversity, Probability, Games
Ref: Monica15
Author(s): McCoy, Leah P; Buckner, Stefanie; Munley, Jessica
Year of publication : 2007
Title: Probability Games from Diverse Cultures
Journal or Publisher: Mathemaics Teaching in Middle School
Volume, Issue, Pages: Vol. 12, No.7, 394-400, March 2007
Reviewer: Monica
Date of Review: April 12, 2009
This article shared six games that can be played in a math class room, from diverse cultures, and gave follow up questions to the games that can help the students make connections to math concepts that they have already learned. I will describe the first game. The first game was called Hubbub which is a Native American game. The game is played with a bowl and dice and is a game of chance. For the Native Americans, they would make their dice out of carved bones, or teeth, or small stones and paint them. The teacher decided to use lima beans for dice and painted one side red and the other side white. So first one of the two players will flip one of the dice to see who goes first. Then the players will put six of the dice in the bowl and shake them. This is how it is scored:
• Six beans alike: 3 points and take another turn
• A second six alike: 6 points and take another turn
• A third six alike: 9 points and pass the turn
• Five alike: 2 points and take another turn
• A second five alike: 4 points and take another turn
• A third five alike: 6 points and pass the turn
• Less than five alike or a nonrepeat on the second or third toss: No points and pass the turn
• Continue playing until one player reaches 50 points
The students can then talk about the probability of getting all six
the same, and also the probability of repeating that three times. They
will notice that it is extremely small and the probability of repeating
those odds are even smaller. The other five games that were mentioned
in this article were: Mancala (African), Toma Todo (Mexican), Dreidel
(Jewish), Ashbii (Native American), and Lu-Lu (Hawaiian).
Keywords: Algebra
Ref: Monica16
Author(s): Usiskin, Zalman
Year of publication :
Title: Why Is Algebra Important to Learn (Teachers, this
one's for your students!)
Journal or Publisher: Algebraic Thinking, Grades K-12
Volume, Issue, Pages: 22-30,
Reviewer: Monica
Date of Review: April 21, 2009
This article was about how algebra is important, not just for school and taking a test, but for everyday life. The author talks about how without algebra: you are kept from m any jobs, you lose control over parts of your life and may need to rely on other people, you may be more likely to make unwise decisions(like financial), and you will not be able to understand many ideas discussed in chemistry, physic, earth sciences, economics, business, and psychology. Then the author says that algebra is the language of generalization. If we were only going to do things once, then we might not need algebra, but we do many things more than once, so that is a reason why algebra is important. Algebra describes patterns and formulas, and some formulas make things easier to determine, like how to multiply fractions.
The author also broke down other reasons why algebra is important. Algebra enables a person to answer all the questions of a particular type at one time. Algebra is the language of relationships between quantities, and algebra is a language for solving certain kinds of numerical problems.
Then the article talked about algebra topics that were important.
They are: Linear Equations, Slope, Exponents, Quadratics, Logarithms,
and Permutations and Combinations.
Keywords: Problem Solving
Ref: Monica17
Author(s): Greenes, Carole E; Spunggin, Rika; Dombrowski,
Justin M.
Year of publication : 1977
Title: Problem-mathics
Journal or Publisher:
Volume, Issue, Pages:
Reviewer: Monica
Date of Review: April 27, 2009
This is a cool problem solving book. It has fun problem solving
activities and it tells the content area of each activity and gives
solutions in the back of the book also with some variation.An example
from the book it's called number neighbor. In this problem, the content
areas covered is mathematical skills and problem solving strategies. In
this activity it explains that like we humans have neighbors, numbers
have neighbors too. Like 2 neighbors are 1 and 3. 2 second neighbors
are 4, because 4 is two numbers away. So the reader is answering some
questions where they want to arrange these numbers as houses on a
street. One question is what is the least amount of numbers you can use
so that one is not by any of its neighbors.
Keywords: Equity/Diversity
Ref: Monica18
Author(s): Lemons- Smith, Shonda
Year of publication : 2009
Title: Equity in the K-12 Mathematics Education: Do we Have
the Will?
Journal or Publisher:
Volume, Issue, Pages: May1-2, 2009, 2009 Minnesota Spring
Mathematics Conference, MCTM
Reviewer: Monica
Date of Review: May 4, 2009
This workshop was about equity and how we need the will to actually make All mean All. The speaker started off talking about how our media puts a ranking on how well students achieve and give statistics on who achieve higher and who is at the bottom of the achievement gap. The speaker read the titles of articles all over the country where they a;; stated in some words that White/Caucasian students perform the best and African American and Latinos do the worse.
The talk then started to talk about what we can do to give all of our students the same educational opportunities. The question was asked why do certain groups perform worse than others. The students who tend to not do as well are ELL students, students of color, and students from poverty. A way that we can help them achieve as high as the other population is to tap into students experiences, families, and communities. When teaching them, we need to let them know that we care about them and a way to do that is to take interest in them. So when we think of activities we can do for the students, we can think of what we can have are students do to incorporate a part of the in the lesson. We can have them bring in family recipes, have projects that have something to do with housing, arts, groceries,candy, music, television, ads, video games, anything that can get the students personally involved.
The teacher also talked about how content matters. A standard test had a question related to bus fair. The problem had something to do with a $1.50 fair for each way transportation daily, and a $65 dollar pass for a monthly bus pass. The question asked which would be the cheapest method to use for a person who had to go to work daily. They wanted the students to say that the $1.50 fair was the best assuming that the worker only worked 5 days a week. Most of the students picked the monthly pass though so the people who made the test wanted to know why most of the students got this question wrong. Most students chose the monthly past because their parents have more than one job, and it did not say that the pass could only be used for one person, so they could share it through the family and that would be cheaper. So in this example, context matter because most students answered a different answer than what the writer was expecting.
Another thing that the speaker said is that everything we do should
be intentional and purposeful. Equity is not a special event and needs
to go beyond hero's and holidays. Equity is not an add on to
curriculum, but it should be a day to day thing.
Keywords: Teaching
Ref: Monica19
Author(s): Mundahl, Stephanie; Nelson, Nicole; Singer,Tim;
Wyberg, Terry
Year of publication : 2009
Title: Surviving Your Beginning Years- Preparing To Teach
Journal or Publisher:
Volume, Issue, Pages: May 1, 2009, 2009 Minnesota Spring
Mathematics Conference
Reviewer: Monica
Date of Review: May 10, 2009
This session was all about preparing for your first years of
teaching. The people who gave the talk were teachers who were in their
first, second and third year of teaching. Some advice that they told us
was to plan in weeks. This way your students always know what will be
done in the class. Also, sometimes it is easier to see where you are
trying to go if you whole unit is planned in advance. Also talking to
other teachers is key, Some things that you as a first year teacher
might be trying to figure out when you can possible get advice from
someone who has already experienced it. Everything you do your first
year is getting you ready for your next year, so keep a binder of
everything you do while teaching so you will have somewhere to start
the next years. Also make multiple plan in case something does not go
as planned. You got to be flexible because sometimes things do not go
as expected.
Keywords: Algebra
Ref: Monica20
Author(s): Burke, Maurice; Erickson, David; Lott, Johnny W;
Obert, Mindy
Year of publication : 2001
Title: Navigating threough Algebra in Grades 9-12
Journal or Publisher: The National Council of Teachers of
Mathematics Inc.
Volume, Issue, Pages:
Reviewer: Monica
Date of Review: May 10, 2009