Keywords: Must Select At Least One, Teaching Strategies,
Ref: Heidemann1
Author(s): Williams, Nancy B., Wynne, Bryan D.
Date: 2000
Title: Journal Writing in the Mathematics Classroom: A
Beginner's Approach
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: Vol 93, Issue 2, pg 132
Reviewer: Heidemann
Date of Review: April 27, 2000
Nancy Wiliams and Bryan Wynne are two high school teachers who decided to try journal writing in their math classes. The article discusses the way they implemented it and the success and failure of their strategy. They decided to test the writing in one class each. They picked the earlier classes for student enthusiasm reasons. One teacher gave five minutes in class to start the journal and the other gave ten minutes. They started with two journals a week, but as the term went on they reduced it to one a week to reduce workload on students and themselves. As the term went on, they reflected over the grades. They noticed that the one allowing only five minutes had more incomplete so they both gave ten minutes.
The article gives the rubric they used and also a copy of the syllabus that they handed out to the students that explained the expectations. Included in the article are ideas for questions. They suggest having two types and alternating. The first is, of course, mathematical questions that has to be solved and justified. The other was affective questions that asked the students opinions of the teaching style, how the student would do it and so on. This seems like a great idea to me. This gives the teacher feedback on his/her style and also gets the students to think about the job the teacher has. It sets a foundation for communication.
Overall this article has lots of information that can be used to set
up journals and gives ideas of what works and what does not. This is
great to read and get a better understanding of how to at least try it.
Keywords: Technology, Geometry, Teaching Strategies
Ref: Heidemann2
Author(s): Purdy, David C.
Date: 2000
Title: Using the Geometer's SketchPad to Visualize
Maximum-Volume Problems
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: Vol 93, Issue 3, pg 224
Reviewer: Heidemann
Date of Review: April 27, 2000
David Purdy discusses the common calculus problem finding out how
to make the box that has the greatest volume possible out of a given sheet
of material. I remember this problem from high school and college, but
Purdy's approach is different. Instead of starting out with the usual
integration and calculus formulas, Purdy uses geometry and technology.
Some teachers have started this problem by giving groups a sheet of paper
and tell them to make different boxes and compare volumes. Purdy has the
idea of using Geometer's SketchPad to solve the problem. The students use
the program to draw patterns. Once the pattern is set up, all the student
has to do is move one line and the whole drawing changes showing the
effect of taking a larger or smaller square out of each corner of the
material. Once the pattern is changed then the student can recalculate
the volume. It can also be set up on the computer to keep track of it as the
student moves the lines. Thus, the student can "discover" the solution
without having to do all the calculus.
This way the problem can be moved down to lower classes, such as geometry
and be used. I still think that
the calculus students need to learn how to do the integration and find the
maximum, but I like this as a way
to introduce the problem. The students' solutions could be used as
comparisons to see how close they get
to the formula. Overall this article presents a great addition to the
maximum-volume problem and saves
paper.
Keywords: Geometry, Activities, Teaching Strategies
Ref: Heidemann3
Author(s): Warkentib, Don R.
Date: 2000
Title: Finger Math in Geometry
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: Vol 93, Issue 4, pg 267
Reviewer: Heidemann
Date of Review: April 28, 2000
This article kind of caught me off-guard. Warkentib is a Californian teacher. He has a unique approach to geometry that I never saw and is definitely not usually in your traditional classroom. He came up with an idea to learn concepts and terms that would help people who learn better visually. He came up with hand signals that were representations of different concepts. One example is vertical angles. If you cross your forearms, you create vertical angles and this visual representation not only helps the students remember the name, but also aids the understanding since you can move your arms to vary the angles. The focus of this idea seems to be the fact that people remember information better if they can associate it with something that they physically do. The article has pictures with a quiz to see if the reader can match the signals with the geometric term or conce
Warkentib did give warning that depending on the location, the teacher has to be careful on deciding what hand signals to use, in order to avoid gang symbols, or making people think of gang symbols. He also mentions the fact of getting together with the principal to decide on suitable signals. Meeting with parents and explaining the idea is something else that he suggests doing.
Included at the end of the article is a few student reviews. They
were interesting to read. Most of them were very supportive saying that
they understood the concepts better and could remember them easier. Only
one states that it did not help at all. The reviews were likely handpicked
to be good on the majority and may not be an accurate representation, but
it still seems like a great idea. People do learn better when they do
something and can associate the word with an action. So I think this is
at least an idea to look into when preparing to teach geometry.
Keywords: Issues, Algebra,
Ref: Heidemann4
Author(s): Feigenbaum, Ruth
Date: 2000
Title: Algebra for Students with Learning Disabilities
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: Vol 93, Issue 4, pg. 270
Reviewer: Heidemann
Date of Review: April 28, 2000
I love this article. Feigenbaum is an instructor at a community college and she has a great attitude. She feels that all people coming into her classroom can learn algebra. This is an important outlook to have considering her students all have learning disabilities (LD). Feigenbaum starts out by describing her students as people that high school had looked at and decided that they would not need algebra or could not do algebra. She goes on to say that the students there know that they need education and math to succeed.
So she explains how she teaches the LD kids. She starts out with defining terms very clearly and analyzes each term and where it came from and what it means. This seems appropriate to do in any classroom and not just a LD class. The students all have to use very proper and clear English to explain the problem and solution when they write it up. Another part she insists on is the writing out of each individual step so the student can see what is happening has a place to go back to check for mistakes if he/she gets the wrong answer. This is wonderful to do so the student can see the concept working.
Her approach is not really all that terrific or earth shattering. I
think that this approach should be used for any math class, especially a
beginning algebra course like the one this is supposed to make up for.
While she is just using good teaching practices, the thing I get out of
this article is the not giving up on the student no matter what label is
given to him/her. I think that is an important thing to use in the
classroom and to realize no matter what, people need math and it is our
job to get it to them.
Keywords: Teaching Strategies, Connections, Algebra
Ref: Heidemann5
Author(s): Misener, Jeff
Date: 2000
Title: Blake's Slope-Intercept Surprise
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: Vol. 93, Issue 3, 242
Reviewer: Heidemann
Date of Review: May 11, 2000
This article describes a teacher's experience when teaching
slope-intercept form. Misener sets this
up by explaining what had been covered prior to slope-intercept. The
previous main topic was arithmetic
series. He described the series with the original term and then the
change to it that multiplied by the term
of the series that you want. (x0 - 2n = xn where x0 is the starting point
and n is the term in the series (1st, 2nd,
3rd, etc.) and xn is the term you want) Then Misener explains that next
he went to teaching slope-intercept.
As he was introducing the subject and asked the class if they could find
an equation to describe the line, a
student, Blake, came up with a way of using the concept of arithmetic
series to solve it. Blake's method was take the slope and the single
point given and to make a series out of it. In order to do that he took
the slope, m, and multiplied it by the quantity x-x1 and then added y1. So
it was y=m(x-x1)+y1. He then multiplied through by the slope and combined
the mx1 and y1 terms. He then had an equation, y=mx+mx1y1, where mx1y1
was a constant. We would call it b. So using this completely different
approach, Blake found another way to get the equation for a line. I
thought this was great. After the teacher figured out the math behind it
and why it worked, he used it in other classes. Not as the primary way to
find an equation for a line, but as an alternative to the slope-intercept
form. This is wonderful because it shows a connection between linear
equations and artihmetic sequences. It's important to show connections
between the topics in our classes.
Keywords: Calculus, ,
Ref: Heidemann6
Author(s): Fiore, Greg
Date: 2000
Title: An Out-of-Math Experience: Einstein, Relativity, and
the Developmental Mathematics Student
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: Vol 93, Issue 3, pg 194
Reviewer: Heidemann
Date of Review: May 17, 2000
This article struck me odd at first. Very odd. Greg Fiore discusses Einstein and his theory of relativity. Two things seemed weird. One that this was in a math journal and not physics, and two, he was proposing teaching this to high school students. When I first began I was thinking this had college physics written all over it. Then I got into the article and realized the potential in it. There are functions, algebra, and all sorts of math. Story problems based on relativity were asking to be used. Looking at it, I feel this still should be an advanced math class in high school. It might also be possible to bring in the physics teacher in on this. He/She could teach the physics behind the theory and you could teach the math. All sorts of possibilities exist in using this theory. Math abounds, and students will definitely have to think and reasoning. With all of these connections and this approach of teaching the math through the application instead of teaching the math and then the application, this is a great idea. Still it might be tough to use.
The end of the article is what really got my attention though. It
discussed Einstein's difficulty in
school, especially math. This is something that can be related to
students having troubles with math. It
could serve as inspiration and motivation. At the very least, it could be
comforting to think that one of the
greatest minds of the 20th century had difficulty with school at one time.
Keywords: Geometry, ,
Ref: Heidemann7
Author(s): Kolpas, Sydney J., Masson, Gary
Date: 2000
Title: Consul, the Educated Monkey
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: Vol 93 Issue 4, pg 276
Reviewer: Heidemann
Date of Review: May 17, 2000
This was a neat article about a toy from the early 1900s. The
article begins by describing Consul, the Educated Monkey. This is a tin
toy made in 1916 that could do multiplication. The person using the toy
only had to place one foot on one factor and the other on the other factor
and the hands pointed to the correct answer. The idea that made this
possible was to put the numbers in a 45-45-90 degree triangle with the top
angle being 90 degrees. The article goes on to propose to use this idea
of a toy for geometry. The idea is to use the toy to teach linkages and
proving that the toy will always show the right answer. This is a
hands-on and practical application of geometry. Instead of just showing
generic linkages and properties of a 45-45-90 triangle, the class could
show why this works and how the toy was developed. They could find other
applications for it such a
Keywords: Activities, Games, Teaching Strategies
Ref: Heidemann8
Author(s): Gaglione, Jeffrey
Date: 2000
Title: Relay Review
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: Volume 93, Issue 4 pg 282
Reviewer: Heidemann
Date of Review: May 17, 2000
This is just a simple idea for a review. Gaglione uses an idea of team relay to review for classes. It's pretty much like it sounds. He divides teams up and has a different set of problems for each team. Each member of the team takes a turn of going to the board and being the scribe. The scribe reads the problem and tries working out the question. Team members can help from they're seats. They are not allowed to go to the board and write or help, but only can yell ideas from they're seats. After the scribe gets done with the problem, he/she goes back to the team and hands off a baton to the next person who goes to the board and does the next problem. After all the problems are done, answers are checked and you can have another round by swapping cards between the teams.
Something I would want to do is to go over the answers after a round
and check out the work and see how it was done. Maybe only have one round
and spend the rest of the time discussing the work. That way there is the
fun of the competition between groups, but there is still some structure.
Do not simply tell the mistakes, but have other classmates talk about what
is right and wrong with the problem. For this there should be guidelines
on how to discuss so that nobody gets called a moron. Try to make sure
nobody feels stupid for getting a problem wrong, but that they understand
what is wrong. That provides a good review and is a fun activity that
will keep kids involved.
Keywords: Teaching Strategies, Reasoning,
Ref: Heidemann9
Author(s): Copes, Larry
Date: 2000
Title: Messy Monk Mathematics: An NCTM Standards Inspired
Class
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: Vol 93, Issue 4, pg 292
Reviewer: Heidemann
Date of Review: May 17, 2000
This is by far one of my favorite articles. It is not written as
an article. It is essentially a manuscript from a class discussion with
thoughts of the teacher as the lesson is going. Copes presents a problem
to the class. The problem presented is about a monk climbing a mountain
in the morning and coming down the next morning. The question is if the
monk leaves at the same time and travels at the same constant pace, will
he be at there be a spot that he passes at the same time each trip. He
presents the problem and lets the class discuss it. While you read the
comments of the students, Copes puts in what is going through his mind.
Thoughts of questions, who he thinks has the idea, how he gets different
students motivated. Not once does he suggest an idea, but he still guides
the discussion. He avoids asking one girl for a while because he thinks
that she might hav
Keywords: Calculus, Teaching Strategies,
Ref: Heidemann10
Author(s): Critchlow, Carol M.
Date: 1999
Title: A Prop is Worth Ten Thousand Words
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: Vol 92, Issue 1, pg 27-28
Reviewer: Heidemann
Date of Review: May 17, 2000
This is a good article discussing props for calculus class. Critchlow mentions props that she used. For cross-sections she used a loaf of bread. It's easy to see that if you take each individual slice and add them up that they will equal the volume of the whole loaf. Each slice should be identical, except the end ones that can be ignored.
She also uses vegetables for solids of revolution. She suggests cucumbers and squash. The best two props I think she suggests for solids of revolution are a fan and a collapsible decoration. The fan is a paper fan that can be opened and it can be suggested what would happen if the fan could be opened the full 360 degrees. She also mentions that certain fans have two different patterns and the break in the patterns could be used to describe a washer. The decoration she mentions is a wedding bell. When it is collapsed it is a two-dimensional object with the straight edge as the axis and the curve is the line being rotated. When the rotation of the line is complete, you have a three-dimensional solid.
This use of visual aids helps describe some important ideas of
calculus. The way I was taught these ideas was by drawings on a
two-dimensional board, which confused me at times and was hard to
visualize. These props are great for visual learners and probably not
just visual learners. It was good to hear a new idea for calculus. Most
of the lessons have to do with making algebra or geometry more exciting
and leaves calculus as it is.
Keywords: Technology, Standards,
Ref: Heidemann11
Author(s): Podlesni, James
Date: 1999
Title: A New Breed of Calculators Do They Change the Way We
Teach?
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: Vol 92 Issue 2 pg 88-89
Reviewer: Heidemann
Date of Review: May 17, 2000
Podlesni discusses the newer calculators with the ability to factor
and do higher calculus. He questions the purpose of them. He comments on
the fact that people want tests rewritten so that these calculators have
to be used. Podlesni asks why should we change the tests. What is the
good of having students knowing how to use the calculator, but unsure if
they know how to factor on their own? He suggests that maybe it would be
wisest to leave the questions as is and have students demonstrate their
knowledge of how the mathematics work. He also asks why the TI-89 has to
look so much like the TI-83 and TI-85. He seems to imply that if people
were to adapt the policy of no calculators with factoring ability and
such, that it would be difficult to enforce since the 89 looks so much
like the 83 and 85. His conclusion is that we should be careful with
using calculators on adv
Keywords: Activities, Problem Solving, Connections
Ref: Heidemann12
Author(s): Fernandez, Maria L.
Date: 1999
Title: Making Music with Mathematics
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: Volume 92, Issue 2 pages 90-97
Reviewer: Heidemann
Date of Review: May 17, 2000
This is a great activity and discovery lesson. Fernandez divides up the class into groups. She gives each group a note from a simple song, such as Mary Had A Little Lamb. She tells them the note and the frequency of the note. They have to take a plastic soft drink bottle and fill it with water and tune it to that note. The groups get TI-82s and a Calculator Based Laboratory (CBL) with a microphone. The students record the sound with the CBL and graph it. They use this graph to learn about the frequency of the note they made and what they have to do to change it to the note they were assigned. She only gave them a brief introduction to frequency and neglected to tell them a few things about it such as frequency is 1 divided by the period. This she allows each group to work through and discover for themselves. She has found out that groups have come up with many ways
I really like this idea of a lesson. This can be anywhere from middle
school all the way through high school. You can also get other teachers
involved. Bringing in the science teacher, physics teacher in high
school, you can get a cross discipline lesson going. That way the
students can see the possible applications of math.
Keywords: History, Issues,
Ref: Heidemann13
Author(s): Norwood, Rick
Date: 1999
Title: A Star to Guide Us
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: Volume 92, issue 2 pages 100-101
Reviewer: Heidemann
Date of Review: May 17, 2000
Mathematical symbols do not get much mention today, but Norwood
leads us through the history of multiplication symbols. He starts with
the traditional x that we all learned in grade school and had to be taught
otherwise because the multiplication x was too easy to get mixed up with
the variable x. Later on we adopted the dot and that was confused with
decimal points. Then we went on to implied multiplication with the use of
parentheses. That worked for awhile until computers came along and did
not know about implied operations. So then we used the asterisk for
computers. Norwood suggests that we use the asterisk as the complete
symbol for multiplication. Start out grade school lessons with the
asterisk being taught as the sign for multiplication. Then stick with it
throughout all of school. That way in is already in use later on when
other symbols will be confused.
Keywords: Activities, Probability,
Ref: Heidemann14
Author(s): Marks, Daniel
Date: 1999
Title: The Big Loser
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: Volume 92 Issue 3 pg 208-213
Reviewer: Heidemann
Date of Review: May 17, 2000
This is an activity that I loved doing as I was reading the article. It has to figuring out the "big loser" of a single elimination tournament. The "big loser" is the team that loses to a team that loses to the team that loses to the team that loses and so on until it is the team that loses in the championship game. Marks uses one bracket of the NCAA basketball tournament to introduce this idea. Taking on region of sixteen teams, and assuming that all the higher seeds win, the team seeded 11th is the "big loser" This is because 11 lost to 6, which lost to 3, which lost to 2, which lost to 1 in the championship game. This is about two-thirds of the teams in the tournament. As the number of teams increase, the closer the "big loser" gets to being exactly two-thirds of the teams. Students than can go on and prove that the "big loser" will be the team seeded two-thirds of t
Another use for this lesson is probability. Rarely do all the higher seeds beat all the lower seeds, so one can assign probabilities to different games. Like a 1 seed beating a 4 seed would be happen with a probability of .7. 2 beating 3 or 1 beating 2 or 3 beating 4 would be .5 and so on with the closer seeds are the closer either team has winning. Then the class can figure out the possibility of 2 winning the tournament. He suggests using only 4 teams, at least for an introduction.
This activity can be used in many ways for math lessons. It is
interesting for those who are into sports and tournaments. It would be
good to use during the NCAA basketball tournament when there is a high
interest in it.
Keywords: Activities, Connections,
Ref: Heidemann15
Author(s): Cox, Pam; Bridges, Linda
Date: 1999
Title: Calculating Human Horse Power
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: Volume 92, Issue 3, pg 225-228
Reviewer: Heidemann
Date of Review: May 17, 2000
This is a good activity that could be used as a combination math and physics class. It uses algebra to calculate horsepower of a student going up a flight of stairs. To start, there is a discussion of horespower and conversions. There is a worksheet to be completed that covers converting what you know into what you are looking for. After this, the students are supposed to have the tools to figure out the original question. They are in groups of 3 with one person as the scribe, one person as the subject climbing the stairs, and one person weighing the subject and the height of the stairs and time taken climbing them.
This is a lesson that could easily be used with a physics teacher with
the idea of force, mass and time and horsepower even. This is a good
lesson that applies the ideas of algebra without telling the students they
are doing algebra in the conversions. This is a great lesson to use as an
assessment of understanding instead of a test.
Keywords: Activities, Statistics, Reasoning
Ref: Heidemann16
Author(s): Friedman, Hershey H.
Date: 1999
Title: Teaching Statistics Using Humorous Ancedotes
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: Volume 92, Issue 4, pg 305-308
Reviewer: Heidemann
Date of Review: May 17, 2000
This is an interesting way to teach the basics of statistics.
Friedman says he uses humor to teach statistics. I am not sure how
funny the stories are, but they do teach the basics. He presents a story
to the class that has to do with a statistical study and contains a fault
in it. The students are to discuss what could have gone wrong with the
study and discover a concept of statistics. One story has to do with
dispersion of a sample. It has to do with the main character, Dr. Ima
Klutz, having to find if the apples from an orchard are sweet enough to
make juice from. Klutz takes 1000 apples from 1 tree, instead of 1 apple
from 1000 trees. The students are expected to figure out what went wrong
with the study. This seems like a good idea, instead of lecture, the
students have to reason out what was wrong. Other stories have to do with
wording of questions, reliabi
Keywords: Issues, Communication,
Ref: Heidemann17
Author(s): Fiore, Greg
Date: 1999
Title: Math Abused Students: Are We Prepared to Teach
Them?
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: Volume 92, issue 5, pg 403-405
Reviewer: Heidemann
Date of Review: May 17, 2000
This article flat out scares me. It has to do with Fiore's experience with two adults in a college math class and how they were abused mathematically. Fiore begins by introducing the class and saying that two students, Terry and Lenore, were very nervous in the class. He was unsure why they were anxious and nervous. So he had the students write a "Math and Me" paper on their experiences in math. The papers he got back from Terry and Lenore were very enlightening. Terry had an experience in third grade where she was sent to the board to solve a problem in the morning and could not sit down until it was solved. She did not know how to do it. Instead of helping her, the teacher kept her at the board all day until class let out. Lenore's paper told of how when she asked for help from her father, he explained it then slapped her and called her stupid when she did not unde
Fiore has two points in why he told these stories. The first is the
importance of the "Math and Me" papers and how they can be used to figure
out what students have experienced and what might work. The other is how
teachers have an influence over the students. Providing encouragement and
help could provide a positive experience for the student and help him/her
understand and appreciate math.
Keywords: History, ,
Ref: Heidemann18
Author(s): Kelley, Loretta
Date: 2000
Title: A Mathematics History Tour
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: volume 93, Issue 1, 14-17
Reviewer: Heidemann
Date of Review: May 17, 2000
This article combines my two favorite subjects, history and math.
Kelley mentions the fact that neither history nor math really cover the
history of math. This is an opportunity for math teachers to take and
use. Discovering the history makes the subject more real. Putting names
and faces to formulas can help make them seem more important. Kelley goes
through on a brief sketch of math history. She covers the Egyptians,
Chinese, and Greeks all briefly. There are so many parts that can be
blown up and used. There are stories that could capture students
imaginations. I think the use of history could make math more exciting
and real to students.
Keywords: Issues, ,
Ref: Heidemann19
Author(s): Jackson, Carol D.; Leffingwell, R. Jon
Date: 1999
Title: The Role of Instructors in Creating Math Anxiety in
Students from Kindergarten through College
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: Volume 92, Issue 7, pg 583-586
Reviewer: Heidemann
Date of Review: May 17, 2000
This article covers math anxiety. It is a study on elementary
teachers. They were asked about
their math experiences. The study revealed that there were three main
spots that caused anxiety. Grades 3-
4 and all of high school and first year in college seemed to be troubling
experiences for people. There were
some recurring themes in all 3 areas. One is that the instructor refused
to go over material again. Another
was the speed, some teachers just went too fast. Students were ridiculed
for not understanding the material.
The one that really repeated itself was that girls do not need math.
These all seem really dumb to me.
What was the teacher thinking? If we want students to enjoy and learn our
subject, ridiculing them and
telling them that they do not need it seems pretty self-defeating. Also,
understanding is required. People
are scared of what they do not know and scared of admitting that they do
not know. In the 3-4 grades
especially, kids want to learn. There is competition in learning. So tap
into that and make sure everybody
understands. If you can hook them at that age, it will be easier to teach
them and keep them involved in
later math.
Keywords: Teaching Strategies, Issues,
Ref: Heidemann20
Author(s): Izen, Stanley P.
Date: 1999
Title: Fearless Learning
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: Volume 92, Issue 9, 756-757
Reviewer: Heidemann
Date of Review: May 17, 2000
Learn from your mistakes is this articles main idea. Izen points out that charging ahead and making mistakes is part of learning. Instead of saying an answer is wrong, ask about it. Find out where it came from and learn from it. People fear math because they are scared of making mistakes in it. So what if you make a mistake? Taking a chance and guessing is when you learn the most. Instead of just having right and wrong answers, use each answer as a lesson. Right ones are examples of what can be done. Wrong ones are attempts that may have gone slightly wrong, or are way off-based. Look at the wrong ones and find out what did not work. Do not be scared of learning. That is all what Izen is saying in his article. Taking chances is what makes it more exciting. Discovering mistakes sticks in a person's mind much more than a formula. So instead of giving mistake a negative connotation, use it to your advantage.