Keywords: Equity/Diversity
Ref: Katie1
Author(s): Allsopp, David; Lovin, Louann; Green, Gerald;
Savage-Davis, Emma
Year of publication : 2003
Title: Why Students with Special Needs Have Difficulty
Learning Mathematics and What Teachers Can Do To Help
Journal or Publisher: Mathematics Teaching in the Middle School
Volume, Issue, Pages: Vol 8. No 6., pgs 308-314
Reviewer: Katie
Date of Review: February 17, 2008
This article chronicles common difficulties students with and without
documented learning disabilities face. The most common four that can be
seen in all classes are attention problems, cognitive problems, memory
problems, and metacognitive deficits. David Allsopp explains each of
these problems briefly with an example related to mathematics and how
the student's problem is perceived versus what the problem
actually is, for example teachers seeing attention disorders as a lack
of focus rather than a focus on too many things all at once. After
these difficulties are discussed, the article moves on to strategies
teachers can use in their classroom to assist students who are having
difficulty with learning mathematics.
The article then moves into an example of an eighth grade teacher who
has a group of students who are achieving at an incredibly low level.
She utilizes a variety of teaching strategies talked about earlier in
the article for students without documented learning disabilities.
Strategies that are used include teaching authentic, meaningful
contexts, finding many practice opportunities, and bringing the class
through examples that move from concrete to representational to
abstract. This teacher brings her class through the steps needed to
work through a story problem and the reader can see a clear example of
how to implement these teaching strategies into the classroom in a
meaningful way.
I found this to be an incredibly helpful article to read, as it
didn't just state what to do in the classroom, but gave an
actual example of how a teacher used the teaching strategies in her
classroom. Also, it is very helpful to have information on problems
students face in the classroom other than documented learning
disabilities. So much of the literature is written about documented
learning disabilities and it is rare to find a well written article,
such as this, that will talk about how to help students who are
struggling in class who don't have a documented learning
disability.
Keywords: Connections
Ref: Katie2
Author(s): Devlin, Keith
Year of publication : 2002
Title: Numbers in the Garden and Geometry in the Jungle
Journal or Publisher: Mathematics Teaching in the Middle School
Volume, Issue, Pages: Vol. 7, No. 8, p. 422 - 425
Reviewer: Katie
Date of Review: February 20, 2008
Devlin suggests that teachers bring students out in the garden to
count leaf patterns, but I think that over a period of time students
would be very bored, so I might use this article to teach with instead
of using the information given and teach by exploration. Possible other
ideas for using this text would include bringing a pineapple in so when
students are reading this article they can verify that Devlin's
claims are true about the Fibonacci sequences. Further along I might
have slides of embryonic animals and then what they look like full
grown so that students can see the geometries of how they are growing
and how that grows into their pelt designs. Again I feel like having
students go and count leaves would be boring for them, especially at a
high school level where they can really begin to understand the
intricacies of the Fibonacci sequence. By high school, students are
mature enough and intelligent enough to read this kind of sophisticated
writing and it doesn'! t need to be reinterpreted by teachers.
By in large, this is an interesting article that gets people thinking
about math in a different form, but instead of giving it only to the
teachers, gives students the chance to read this for themselves.
Keywords: Representations
Ref: Katie3
Author(s): Peterson, Blake E.
Year of publication : 2006
Title: Linear and Quadratic Change
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: Vol. 100, No. 3
Reviewer: Katie
Date of Review: February 24, 2008
Peterson’s “Linear and Quadratic Change” is an incredible article that shows that the stereotypes about American versus Japanese schools aren’t necessarily true. The conclusion of this article isn’t that there is a cultural effect that makes learning different in the two countries, but rather when we use engaging lessons and rich mathematical problems students thrive and grow as young problem solvers.
This article chronicles a problem that has quadratic and linear applications in it, both a group of students in America and a group of students in Japan worked on this problem. These students chose different parts of the problem to explore, from perimeters (a quadratic extension) to change in leftover space (a linear extension). The classes tried to figure out different extensions of this problem, representing different applications within the problem.
This is a very optimistic article about American education, which
says that yes, we can catch up with the rest of the world. The problem
is not with our culture, but rather with the types of lessons we are
using with our students. This is an excellent article for new teachers
and old teachers alike, and I would highly recommend reading this. We
can make a difference in our education system, we just need rich
problems.
Keywords: Proof, Geometry, Communications
Ref: Katie4
Author(s): Gole, Andy
Year of publication : 2003
Title: Sherlock Holmes, Geometry Proofs, and Backward
Reasoning
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: Vol. 96, No. 8, pgs 544-546
Reviewer: Katie
Date of Review: February 26, 2008
I found this article fascinating at it brings together literature to come up with an idea for solving mathematical proofs. The process of working backwards in math is something that comes fairly naturally once we hit the college level and are used to doing it, but learning the process of working backwards is a difficult skill to develop. Gole’s “Sherlock Holmes, Geometry Proofs, and Backward Reasoning” shows a two column proof quite common in high school geometry classes. There is a dialogue between a teacher and a student and the teacher asks the student questions to get the student thinking in a backwards reasoning way. After this dialogue there is another problem which shows the difference between forward and backward thinking and how in some cases backwards thinking is the most appropriate option.
Sherlock Holmes has a quote about solving mysteries by looking at the end result and looking backwards step by step until you get to what you want, in his case, a guilty suspect. This is surprisingly similar to how we can work with math. We know the end result, for example to prove two angles are congruent, then work backwards with how to prove it, then find the pieces used to prove it, and solve it using backwards reasoning. At this stage in my mathematical career I don’t need to think about working backwards, it comes naturally, but it’s extremely difficult to wrap our minds around when we start to think this way. It’s a complete 180 from what we are used to at this point, so it takes good questions from the teacher and time to let students struggle a bit to finally grasp this important way of thinking and reasoning through a problem.
It takes time to understand how to reason through a problem and I
find that this is an incredibly helpful article for teachers to read.
The dialogue gives good ideas for questions we should be asking to help
this new kind of reasoning. This is a very good example of how to help
students through this new type of learning. Highly recommended! Read
this!
Keywords: Communications
Ref: Katie5
Author(s): Koellner_Clark, Karn; Stallings, L. Lynn; Hoover,
Sue A.
Year of publication : 2002
Title: Socratic Seminars for Mathematics
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: Vol 95, No. 9, pgs 682-686
Reviewer: Katie
Date of Review: March 2, 2008
“Socratic Seminars for Mathematics” shows an entirely new way to communicate mathematics to students. It is very unusual for mathematics to be discussion based, but this article shows an entirely discussion based way to run a mathematics classroom. There are a few examples of how to teach functions using a Socratic seminar. Socratic seminars are run by a teacher asking thoughtful questions and students discussing possible answers. The classroom is set up in a circle so that everyone in the class can see each other and discuss. There are guidelines to Socratic seminars and how students are to treat each other. However, the teacher must be careful to communicate through questions so that the students figure out problems for themselves instead of being given an answer.
I found this to be a fascinating article, I had never thought of
using this in one of my classes. I’ve always found it to be very
difficult to figure out how to incorporate discussion into a math
class, but this is a perfect way to accomplish just that. I love the
idea that we can communicate strictly through questions, and then the
students can communicate with each other and puzzle through problems
together. This is a great article that teachers should read, because
it’s completely different than the typical mathematics classroom.
Keywords: Number and Operation, Games
Ref: Katie6
Author(s): Burkhart, Jerry
Year of publication : 2007
Title: Integer Target: Using a Game to Model Integer
Addition and Subtraction
Journal or Publisher: Mathematics Teaching in the Middle School
Volume, Issue, Pages: Vol. 12, No. 7, pgs. 388-392
Reviewer: Katie
Date of Review: March 9, 2008
Burkhart’s “Integer Target: Using a Game to Model Integer Addition and Subtraction” models a fun way for students to learn how to add and subtract positive and negative numbers. The students work with number cards with integers on them and a number line. Students begin by thinking about the concept of taking away different number cards and what that does to the total value of the number cards, for instance taking away a negative number makes the total value more positive. Similarly, adding another negative number card will make the total value go more negative. Once the students have worked with these integers, they start playing a game called Integer Target. A group of students is given an integer on the number line that is their target, they then use their number cards to find as many ways as possible to hit this target. They can add more cards or take away cards they already have to get to this target. This game helps them understand how to add and subtract all integers, by modeling what makes things go in the positive direction and what makes things go in the negative direction.
I think that this is a very interesting concept that is quite useful
for students who are beginning to learn about adding and subtracting
integers. When students are beginning to learn about subtracting
negative numbers, they usually just follow a rule that changes
everything to adding a positive number, but in this case the students
can actually see that taking away a negative number makes their sum
more positive. I think that this is a great way to teach students about
integer addition, and would be a great resource for teachers to have.
Keywords: Algebra, Activities, Games
Ref: Katie7
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, pgs 26-31
Reviewer: Katie
Date of Review: March 11, 2008
Menon’s “Motivating Activities That Lead to Algebra” brings about the idea that students do not have to think about algebra in a scary computational way, but rather there are fun, interesting applications with algebra that can get students interested and excited about algebra. There are games and activities that seem like mind reading, where someone can perform a sequence of math, for instance take your age add 20 then divide by 4, etc, in which students can do algebra to figure out what a person’s age is, and other fun puzzling games. The games can be changed for different skill levels, either making the algebra easier or adding in more advanced algebra to help differentiate the instruction of beginning algebra. These activities are great motivating strategies to get students excited about learning algebra. If we tell students that they’re going to learn about factoring, a lot of them won’t think it’s exciting, but if they hear that they can learn how to make people beli! eve they are a mind reader that will get the students excited.
I think that these activities would be great in a higher level
middle school classroom and/or a lower level high school classroom.
There is a very common difficulty in mathematics teaching in that
occasionally it’s extremely hard to motivate students and teachers need
to figure out a way to get students engaged in what they are learning.
These tips are excellent for beginning to teach algebra, and I would
whole heartedly use them at the beginning of the year in an algebra
classroom. This is a great article with some great tips for teaching in
an algebra class and is well worth a read.
Keywords: Technology, Connections, Games
Ref: Katie8
Author(s): Baker, Paul L.
Year of publication : 2003
Title: Using FreeCell to Teach Mathematics
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: Vol. 96, No. 6, pgs. 406-410
Reviewer: Katie
Date of Review: March 15, 2008
Baker's `Using FreeCell to Teach Mathematics' is an interesting, fun article. He talks about using the computer game FreeCell to show students different parts of mathematics like probability, proof, and theorems. Students today play computer games and video games almost obsessively and bringing their interests to the classroom is a great way to engage students. Using the game of FreeCell, Baker's students can discuss similarities and differences to other deep mathematical problems, for example to the Bridges of Konigsberg and the four color theorem.
I find that this article is a nice example of finding a way to
relate to students and give them a gateway to connect their interests
to what happens in the classroom. However, I do not know what kind of
class I would use this kind of activity in; there ian'r a clear
application to algebra, geometry, or calculus. I can see how this would
be very applicable to a classroom setting like our college course,
Gateways to Mathematics, with fun applications of math. This is a nice
way to connect to students, but I think it could be hard to implement
into a high school classroom setting.
Keywords: Geometry, Activities, Problem Solving
Ref: Katie9
Author(s): Pandiscio, Eric A.
Year of publication : 2002
Title: Alternative Geometric Constructions: Promoting
Mathematical Reasoning
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: Vol. 95, No. 1, pgs 32 - 36
Reviewer: Katie
Date of Review: March 17, 2008
Pandiscio’s “Alternative Geometry Constructions: Promoting Mathematical Reasoning” highlights a geometry lesson that is a prime example of what America’s mathematics curriculum needs to grow the way we are hoping it will grow. He discusses three geometric construction tools, a Mira, a 3 x 5 index card, and a two edged straightedge, and talks through three geometric constructions. Using only these tools he can construct a perpendicular bisector, a parallelogram given two adjacent sides, and given one side constructing an equilateral triangle. In order to create these constructions students needs to have a strong knowledge of different properties of geometric figures and an adventurous mind who can make mistakes and learn from them. This is a fabulous activity for a geometry class to enforce geometric rules and to help students reason through their prior knowledge to understand why these constructions can be made with only one construction tool.
I’m curious as to why there aren’t more lessons like these in our
mathematics classroom. I feel that this is an incredible lesson that
promotes the higher level thinking that our country is striving to
achieve. This kind of thing is never tested on a standardized test
because it requires problem solving, reasoning, and pulling together
many geometric properties, it’s “too complicated to use on a test”.
These constructions can require so much thinking on the part of the
students, a teacher doesn’t have to stand up at the board and say,
“this is how you do it”. Students can puzzle through this, try out many
things to see what works, and truly reinforce the knowledge they
already have. This is an absolutely fantastic article and lesson, any
teacher who is teaching a geometry class should put this lesson aside
in their repertoire, it is that great of a lesson.
Keywords: Probability, Problem Solving
Ref: Katie10
Author(s): Kahan, Jeremy A. and Wyberg, Terry R.
Year of publication : May 2003
Title: Problem Solving Can Generate New Approaches to
Mathematics: The Case of Probability
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: Vol. 96, No. 5, pgs 328-332
Reviewer: Katie
Date of Review: April 2, 2008
Kahan and Wyberg’s “Problem Solving Can Generate New Approaches to Mathematics: The Case of Probability” is a fantastic article that explores different ways to solve probability problems, specifically the World Series problem. They go through how students can solve these problems using simulations, trees, and generating functions to all come up with the same answer. Then they give possible extensions of the problem such as if the two teams are not equally matched, but rather one has a greater probability of winning every game. They believe that teaching all three methods is a more powerful way to teach and is much more effective at reaching all students in the class. Through the multiple approaches there is a clear indication of how Pascal’s triangle, the binomial theorem, and the Bernoulli distribution are all related to probability. All these methods help students find which way is most effective, both as a generalization and internally. Kahan and Wyberg conclude that p! roblems like these can be considered vehicles in mathematics that can travel different routes that end in the same destination, which is a fabulous way to explain this type of problem.
This is a fantastic article and a must read for all future teachers
who may or may not teach a class in probability. The outlook on rich
and deep problems in this article is astounding and wonderfully
refreshing. It doesn’t talk about the problems and what needs to be
fixed in mathematics education today, but rather focuses on their
car-route-destination analogy, which is a wonderful way to look at
math. This problem is well worth using in a classroom, both because it
is a useful and engaging problem, but also it shows how mathematicians
work, and that there is not necessarily one correct way to solve a
problem, but rather that three mathematicians can look at the same
problem and attack it in three separate ways and all result with the
same solution. This is an honest, refreshing article about great
probability problems and extensions, a must read!
Keywords: Problem Solving, Research
Ref: Katie11
Author(s): Cuahnwe, Jason
Year of publication : May 2003
Title: Problem Solving The Problems of Society
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: Vol. 96, No. 5, pgs 320 - 323
Reviewer: Katie
Date of Review: April 7, 2008
Cushner’s “Problem Solving the Problems of Society” follows a high school mathematics class that spend the entire year working on a real world problem. They looked at a non-profit called the Snowboard Outreach Society (SOS) who takes at-risk youth and turns their lives around through snowboarding. This company had a huge expansion possibility but at the time the infrastructure could not handle the growth. This math class then took this real life situation and analyzed this business all year long. They learn how to project growth and did that for the company, analyzed budgets, and analyzed all the data the company gave the class. By the end of the year the students had formulated a plan to help SOS grow and develop to meet what was possible rather than what their current infrastructure allowed. These students worked together in a real world situation and did real world problem solving and high level mathematics and data analysis.
I think that this is a fabulous way to work with a class that you have complete control over, something like operations research or independent study or basic math, that doesn’t have a set curriculum. This is an excellent way to run an open classroom, letting students problem solve actual problems that they might encounter in the real world. This group of students were not considered the best students and were in a remedial math class and ended up doing this complex mathematics. The reason this went over so well and the students learned so much was because the math they were doing had practical applications and students could problem solve in whatever way they could. I would definitely run a class like this if I had the opportunity, of course I wouldn’t use the same company, but if there was a similar type of company who our class could analyze that would be fantastic.
Keywords: Geometry, Proof
Ref: Katie12
Author(s): Quinn, Robert J., Ball, Tom S.
Year of publication : August 2007
Title: Explore, COnjecture, Connect, Prove: The Versatility
of a Rich Geometry Problem
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: Vol. 101, No. 1, pgs 8-11
Reviewer: Katie
Date of Review: April 7, 2008
Ball and Quinn’s article, “Explore, Conjecture, Connect, Prove: The Versatility of a Rich Geometry Problem” showcases a fantastic geometry problem that can be used in a high school classroom. This problem is about a man rowing from a dock to another dock where his lines of sight to both docks are kept at a ninety degree angle, students are to find the path that this man rows. Throughout the article, Ball and Quinn discuss stopping points and things that students will run into, and how, as a teacher, what we can do to help that won’t simply give them the answer to the problem. The authors suggest letting students use some kind of right angle to tract a possible path from one dock to the other, which will lead them to believe that the path is a curve, or more correctly a circle. Then many students will assume that the path is a circle, and try to prove the path is a circle, which of course they cannot do. The authors then chronicle multiple correct proofs that students of all ability levels can find. This leads to tiered learning where if one student quickly figures out one proof, they can be asked leading questions about finding other correct proofs.
This problem is a fantastic problem that leads students to use true
critical thinking skills. They need to explore what possible paths look
like, come up with conjectures, then try to use their background
knowledge to come up with a working proof. The different proofs that
one can come up with are varied, some are more difficult that others,
and some are fairly attainable, but the most important part with this
is that all students can come up with these proofs, especially when
their teachers ask meaningful questions. This is a great article that
has a thought-provoking problem that can and should be used in geometry
classrooms.
Keywords: Teaching Strategies, Communications,
Ref: Katie13
Author(s): Meel, David E., Gyurko, Deborah, Gaspar, Michelle
Year of publication : August 2006
Title: A Little-Used Art of Teaching: The Case of
Storytelling
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: Vol. 100, No. 1, pgs 64-68
Reviewer: Katie
Date of Review: April 13, 2008
Meel, Gyurko, and Gaspar’s article, “A Little-Used Art of Teaching: The Case of Storytelling” profiles a very rare method of teaching, storytelling. The premise behind this article is that it is becoming common place for students in high school classrooms to think math class and math teachers are boring. They give two examples of types of problems that can be introduced through storytelling, both solving equations with radicals through a princess story and trig functions using an adaptation of the Three Billy Goats Gruff. Using stories to introduce a unit or method of solving some kind of problem is a fun way to get students engaged in what they’re doing in math class.
I think this is a useful article for teachers to read. This is a
unique teaching style, that could be beneficial to all math teachers,
as a way to liven up and make a more engaging atmosphere in the
classroom. The two stories provided in the article are clearly not the
only two stories that could be told to introduce or further along a
unit. There are many extensions to this, not only extensions in
storytelling, but also extensions into other teaching styles. If we can
find a way to teach mathematics through storytelling, there is no end
to the teaching styles we can use in our classroom.
Keywords: Technology, Problem Solving
Ref: Katie14
Author(s): Erbas, Kursat A., Ledford, Sarah D., Orril, Chandra
H., Polly, Drew
Year of publication : May 2005
Title: Promoting Problem Solving across Geometry and Algebra
by Using Technology
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: Vol. 98, No. 9, pgs 599-603
Reviewer: Katie
Date of Review: April 16, 2008
“Promoting Problem Solving across Geometry and Algebra by Using Technology” discusses how by using multiple different technologies on the same problem and enhance students understanding of a problem and the mathematics behind it. The authors of this paper discuss a problem involving walking a rectangular field where walking the diagonal of the field is forty more units than walking along two of the sides. Students then use Geometers Sketchpad, spreadsheets, graphing calculators, and CAS to see how to manipulate data to figure out different lengths of the sides of the field that would be correct answers to this problem. By using these technologies students can see different ways of presenting data, and can come up with correct formulas for how to solve this problem.
I feel that this is an interesting article with some great ideas.
Technology is a wonderful tool to use in the classroom and by using
multiple technologies for one problem students can learn even more.
However, I feel that depending on how many technologies one uses in the
classroom there can be such a thing as too much use of technology. If
we use technology for the sake of it, then it lessens its value. I feel
that using multiple technologies would be incredibly helpful, but we
need to tread a very fine line between what is worthwhile and what is a
little bit overkill, and in the end would end up boring the students.
For instance using a CAS and graphing calculator can do fairly similar
things and using both may not be necessary. So, if we have the means to
have multiple technologies in a class, that would be fantastic, but we
need to be careful to make sure that there is meaning behind which
technologies we use.
Keywords: Puzzles, Activities
Ref: Katie15
Author(s): NCTM
Year of publication : 2004
Title: Figure This!
Journal or Publisher:
Volume, Issue, Pages: http://www.figurethis.org/index.html
Reviewer: Katie
Date of Review: April 20, 2008
Figure This! is a mathematical websites for families to explore together. There are challenge problems that are posed and families can look at charts and graphs, look at data, try experiments as a family, and learn real life applications of mathematics as a family. There is a nice teacher index, so that teachers can incorporate this website into their curriculum as a way to get families more involved. There is also a family corner where parents/guardians can learn how to help their students with homework and studying, there are applications of literature that math pops up in and families can read together. This is a website noted by both NCTM and NSF for providing a quality resource for mathematics outside of the classroom.
Keywords: Connections, Equity/Diversity, Issues
Ref: Katie16
Author(s): McCoy, Leah P.
Year of publication : February 2008
Title: POVERTY, Teaching Mathematics and Social Justice
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: Vol. 101, No. 6, pgs 456 - 461
Reviewer: Katie
Date of Review: April 22, 2008
This article discusses incorporating real life social issues into the mathematics classroom, specifically issues with poverty. There are three project ideas dealing with poverty that can be done in a mathematics classroom in which students can learn high level mathematics, but also discuss the hard issues of poverty. The first project is creating a budget for a family who is right on the poverty line, so according to the government is livable, and seeing what needs to be budgeted for, and what needs to be sacrificed. The second project includes making charts and graphs of different demographics of poverty and where high levels of poverty are located. The final project is looking at different school districts and their poverty status and creating scatterplots on their success on statewide tests. Students make linear regression models and to analyze this data on how poverty status can affect test scores.
Unfortunately, math has a bad rap for being a class where students learn formulas and how to solve equations and is not a place to learn about social issues or effect social change. This article shows that this stereotype need not be true, that social change can, in fact, happen in a math class. Students will get engaged and interested in this subject and will bring a lot of their personalities to the table when working on these projects. There is no place in these projects that a student would say, I’d never use this in real life, what good is this anyway. These projects hit a lot of the NCTM standards and are fantastic ideas for extending a unit or concluding a unit. Overall, this is a fascinating read with a lot of great ideas. Keywords: Connections, Problem Solving, Research
Ref: Katie17
Author(s): Edwards, Thomas G., Chelst, Kenneth R.
Year of publication : September 2007
Title: Purchasing a Used Car Using Multiple Criteria
Decision Making
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: Vol. 101, No. 2, pgs. 126 - 135
Reviewer: Katie
Date of Review: April 27, 2008
“Purchasing a Used Car Using Multiple Criteria Decision Making” chronicles a series of lessons where students work through a difficult decision that they might be making such as buying a car, picking a part time job, choosing a college, and more using a process called MCDM, multiple criteria decision making. This involves placing numerical weights on each part of a decision, and then creating mathematical formulas with these weights to decide on the best option for the decision. Each weight is decided on by individual preference so each person’s decision is unique, so what may be the best car/job/college for one person may be completely different than everyone else in the class.
I think that this is a very good series of lessons for students, especially students who keep asking when would they ever need what they’re learning in math class. This is a very applicable piece of mathematics that every student would be engaged in and would find useful. I find that this could work very well in any classroom if there is an extra week or if there is a unit on analyzing data. This would be perfect in a sheltered math class to get the students interested and engaged in the subject as well. It’s a great idea with a very clear cut outline given, a very useful article to read.
Keywords: Connections, Problem Solving, Puzzles
Ref: Katie18
Author(s): Howe, Roger
Year of publication : February 2002
Title: Hermione Granger's Solution
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: Vol. 95, No. 2, pgs. 86-89
Reviewer: Katie
Date of Review: April 30, 2008
If you want a perfect lesson plan for a substitute, Hermione Granger’s Solution is the perfect article. This article chronicles a famous passage from Harry Potter, one in which Hermione, one of the characters solves a logic puzzle involving potions. This article gives the clues and then goes through the steps Hermione may have taken to solve the puzzle. The actual book does not go into detail about how she solves this problem, and I know when I was reading it I was always curious how she knew which bottle held which potion. This article shows how she knew.
Harry Potter has become iconic for today’s generation and I feel that it will be for years to come as well. This article will engage students and they will learn some interesting things about logic and problem solving. This article is easy enough for students to read, with challenging enough mathematics, and interesting enough to keep the students engaged. This is perfect for planning a lesson for a substitute. A substitute can hand this article out for students to read and puzzle through either individually or in groups. It’s a fascinating article for people who have read Harry Potter. For those who haven’t it is a very interesting logic puzzle to work through, and quite worth a read.
Keywords: Curriculum, Planning
Ref: Katie19
Author(s): Coxford, Arthur F.
Year of publication : 1991
Title: Addenda Series, Geometry from Multiple Perspectives
Journal or Publisher: NCTM
Volume, Issue, Pages:
Reviewer: Katie
Date of Review: May 5, 2008
The Addenda Series, Geometry from Multiple Perspectives is a fantastic resource to include on a mathematics teacher’s shelf. This particular addenda book breaks down different areas of high school geometry, like polygons, solids, and similarity, into multiple perspectives and gives examples of how to teach from these different views. They give ideas about how different students may look at different geometric problems and how to pose problems to fit these different perspectives. There are certainly hundreds of other applications than those given in the book, but it’s a very good starting point, especially for teachers who are beginning to teach a standards based curriculum rather than a skills based curriculum. Throughout the book there are great teaching tips and ideas that can be used in the classroom with a bolded, “Try This” heading. There are also little, “Teaching Matters” and “Assessment Matters” headings as well reminding teachers about appropriate teaching strate! gies and assessments for a curriculum taught specifically toward multiple perspectives.
This is a great book that is, like I said, extremely useful for all
kinds of teachers. I think it is especially important for beginning
teachers or teachers who are switching curriculums or teaching styles
to a more problem solving, standards based method. There are excellent
tips that can be used to assist in lesson planning and possible
assessment tools as well. It’s a fantastic resource, which makes sense
as it was put out by NCTM.
The Navigations book, Navigating through Geometry is a really nice extension of the Principles and Standards book that NCTM put out, which makes sense since the Navigating Series is also put out by NCTM. This Navigations book begins quite similarly to the PSSM section on geometry talking about standards and some specific examples of how these standards could be met in a classroom setting. After this brief introduction the Navigations book goes into Lesson Plans and activities that can be used in the classroom to meet geometry standards. The end of the book has a black and white activity sheet for each activity discussed in the book.
At first I thought that this was cheating a little bit, just being
able to lift ideas off of this book, but the more I thought about it
the more I realized that this is exactly what teaching is. We take
other people’s ideas, give them credit for the idea, and tweak the
activity or lesson so that it fits with what we are trying to
accomplish in our own classrooms. NCTM puts these lessons out because
they know that they will work and are engaging rich mathematical
lessons. This would be great to put in a math department library that
teachers could browse through if they are looking for a lesson, but
can’t come up with an idea that they really like. There are tons of
ideas for all different aspects of geometry and this Navigations Series
is an excellent resource.