that math is cumulative. If you don’t go to class you will miss
important material that will be used in later sections and important
announcements. Get to Class On Time.
Sometime important announcements are only given during the first few minutes of a class. LISTEN During Class.
order to get something out of the class you need to listen while in
class. Often this can be difficult to do but it is very important.
Sometimes important ideas will not be written down on the board, but
instead just spoken by the teacher.
Watch for things
the teacher emphasizes, even if just in words. This often means the
teacher thinks it’s important. The more important that teacher thinks a
topic is, the more likely that it will show up on the exam! Take Good Notes.
to write down everything that teacher puts on board. It may seem easy
when watching the teacher, but it often is not so easy when it comes
time for you to do it. A good set of notes will help remind you how to
do these problems. For some teacher writing down everything may be
difficult. In these cases you should try to write down as much as
Note as well that this seems to contradict the
previous tip. It is often hard to both listen and take a good set of
notes. This is something that one often only gains with practice. You
need to be able to listen while you are writing down the important parts
of the lecture. Ask Questions.
If you don’t understand something then ask your teacher. Chances are you are not the only one who doesn’t understand. Listen When Others Ask Questions.
other students ask questions make sure you listen to both the question
and the answer. It may be that the student asking the question thought
of something that you didn’t think of. Review Notes After Class.
each class you should review your notes. Note the topics that you found
confusing and formulate questions that you can ask your teacher or
tutor to help you understand the topic. Make a Set of Index Cards.
a set of index cards with important formulas and concepts on them. You
can carry these around with you to look over when you’ve got a few spare
minutes. Use them to help you memorize the important formulas and
concepts. Note Due Dates. Write down the due dates for homework and dates for exams someplace you’ll see them so you don’t forget about them. Budget Adequate Time For Studying/Homework. It often takes more time studying mathematics to learn the subject than you may require in other classes. Do Homework After Each Class.
the end of each class budget some time to look over the homework from
that days lecture and attempt to do it Doing this will allow you time to
really work at understanding the concepts covered that day. Do not wait
until the last minute to do the homework as this often results in an
incomplete homework set and an incomplete understanding of the concept. Do Homework Without Notes and Book.
the first few homework problems, put your notes and book up and try to
do the remaining problems without referring to your notes and/or book.
In most cases you will not have these during your exams so get used to
doing problems without them. Do More Homework.
not limit yourself to just the homework that your instructor assigns.
The more problems that you work the better off you’ll be. Practice, Practice, Practice.
as much as possible. The only way to really learn how to do problems is
work lots of them. The more you work, the better prepared you will be
come exam time. Persevere.
will not just instantly get every topic that is covered in a math
class. There will be some topics that you will have to work at before
you completely understand. The only way to really grasp some topics is
to go home and think about it and work some problems. You will often
find that after a little work a topic that initially baffled you will
all of a sudden make sense. Keep Old Homework and Exams.
not throw away homework and exams once you get them back. The homework
is a good source of study material for exams and both the homework and
exams is a good source of study material for comprehensive final exams
(if you’ve got one). Don’t Forget Your Textbook.
you get stuck on a topic that was discussed in class do not forget that
you do have a textbook. Often the text book will contain examples not
worked in class and/or a different approach to a problem. Seek Help If You Need It.
you are having trouble with your maths class you have many options open
to you and you should take advantage of them. You can go to your
tescher’s office hours, go to the tutoring room or hire a tutor to get
Most of the mathematical notation in use today was not invented until the 16th century. Before that, mathematics was written out in words, a painstaking process that limited mathematical discovery. In the 18th century, Euler was responsible for many of the notations in use today. Modern notation makes mathematics
much easier for the professional, but beginners often find it daunting.
It is extremely compressed: a few symbols contain a great deal of
information. Like musical notation, modern mathematical notation has a
strict syntax and encodes information that would be difficult to write in any other way. Mathematical language can also be hard for beginners. Words such as or and only have more precise meanings than in everyday speech. Additionally, words such as open and field have been given specialized mathematical meanings. Mathematical jargon includes technical terms such as homeomorphism and integrable.
But there is a reason for special notation and technical jargon:
mathematics requires more precision than everyday speech. Mathematicians
refer to this precision of language and logic as "rigor".
Rigor is fundamentally a matter of mathematical proof. Mathematicians want their theorems to follow from axioms by means of systematic reasoning. This is to avoid mistaken "theorems", based on fallible intuitions, of which many instances have occurred in the history of the subject.The level of rigor expected in mathematics has varied over time: the Greeks expected detailed arguments, but at the time of Isaac Newton the methods employed were less rigorous. Problems inherent in the definitions
used by Newton would lead to a resurgence of careful analysis and
formal proof in the 19th century. Today, mathematicians continue to
argue among themselves about computer-assisted proofs. Since large computations are hard to verify, such proofs may not be sufficiently rigorous. Axioms in traditional thought
were "self-evident truths", but that conception is problematic. At a
formal level, an axiom is just a string of symbols, which has an
intrinsic meaning only in the context of all derivable formulas of an axiomatic system. It was the goal of Hilbert's program to put all of mathematics on a firm axiomatic basis, but according to Gödel's incompleteness theorem every (sufficiently powerful) axiomatic system has undecidable formulas; and so a final axiomatization of mathematics is impossible.
Nonetheless mathematics is often imagined to be (as far as its formal content) nothing but set theory in some axiomatization, in the sense that every mathematical statement or proof could be cast into formulas within set theory.
Recently, on the Free Technology for Teachers Facebook page
someone asked for suggestions for math resources for grades 7-12. That
covers a broad range of topics in math, but I've done my best to cobble
together a list of resources that I think will help middle school and
high school math teachers and their students. I have not included the
obvious option of Khan Academy.
Get the Math is
a super website designed to provide teachers and students with
Algebra-based mathematics challenges. Get the Math tries to put the
challenges in the context of the "real world" scenarios of fashion
design, video game design, basketball, restaurant management, movie
special effects, and music production. Get the Math features
short videos of professionals explaining and showing how mathematics is
used in their professions. After watching the videos students try to
complete a series of challenges based upon the work done in the
professions of fashion design, video game design, and music production.
For example, after watching the Math in Fashion video students have to design a shirt to match a specific price point
A couple of months ago Curriki released a series of six PBL geometry projects that could make geometry interesting and fun for high school students.Curriki's new geometry course features
six PBL projects. Each of the projects is aligned to Common Core
Standards. The course is not a self-directed course for students. The
course is designed to be taught by mathematics teachers who want to
incorporate PBL. The projects in the course can be used in sequence or
used as stand-alone units. All materials needed for leading the projects
are included available on the Curriki site. You will have to create an
account and sign-in in order to access the materials. Curriki accounts
a service that aims to help middle school mathematics teachers discover
sample math problems aligned to Common Core standards. To find problems
on Opus search by entering a topic and selecting a grade. You can also
find problems by clicking the "browse the Core directly"
link on the Opus homepage. Either way when you find a problem you can
save it to your free Opus account where you can then generate a Word doc
or Google Document of all of your saved problems. You can also create
an answer sheet in your Opus account.
a service that teachers can use to develop interactive mathematics
worksheets. Through MathDisk's "Math Builder" tool you can design
mathematics models that your students can use online. The models and
worksheets you develop online can also be downloaded to use offline if
you also install the MiBook software on your desktop or on your Android
device. If you don't have time to create new materials, the MathDisk gallery
has pages of models and worksheets that you can choose from. Everything
in the gallery, like everything you create through MathDisk, can be
downloaded and or embedded into your own website or blog.
a service that offers an online mathematics program designed to
supplement your in-classroom mathematics instruction. All of the
problems in TenMarks' bank of more than 20,000 are aligned to Common
Core standards. Within TenMarks teachers
create class rosters and accounts for their students. After creating
rosters teachers can assign practice problems to students. Teachers can
assign problems based on the Common Core Standards that their students
are trying to reach.
If you use GeoGebra in your classroom, you should bookmark GeoGebraTube. GeoGebraTube is a community site for teachers who teach with GeoGebra to
share and find a wide range free resources. On GeoGebraTube visitors
will find user-created tutorials, lessons, and worksheets. Visitors can
search for resources by age group, language, and material type. All
materials are freely available for noncommercial re-use.
Math Open Reference is a free online reference for geometry teachers and students. Math Open Reference features animated and interactive drawings to demonstrate geometry terms and concepts. The table of contents on Math Open Reference is
divided into four basic categories; plane geometry, coordinate
geometry, solid geometry, and function explorer tools. Click on any
subject in the first three categories to find definitions, examples, and
interactive drawings. In the function explorer category users can
select linear functions, quadratic functions, or cubic functions to
explore how changes in variables affect the graphed output.
Dan Meyer has a site called 101 Questions
on which he is sharing images and videos as prompts for developing math
questions. Each image and video has a 140 character field in which you
can enter your question. Questions are compiled and can be Tweeted. Take
a look at the top 10 to get a feel for what you will find on 101 Questions. I've embedded one of the videos from 101 Questions
below. I won't pretend to be able to explain the larger purpose of the
site as well as Dan does, so I'll just encourage you to go read his blog post about it. And if you need more background on who Dan Meyer is, watch his TED Talk Math Class Needs a Makeover.
a free site featuring arithmetic and algebra lessons. On ULearniversity
you can watch tutorial videos and practice the concepts taught in the
videos. ULearniversity provides instant feedback on your practice
problems. As a registered ULearniversity user you can track your
Math Shorts is the latest addition to Planet Nutshell's line-up of animated educational videos. Math Shorts
will eventually have twenty videos in the series. Right now the series
contains eight animated videos for elementary school and middle school
students. Each of the videos has a Common Core standard aligned to it.
All of the videos have supporting materials from PBS Learning Media
attached to them. The first video in the series is embedded below.
I have never taught math and I'm open to suggestions for resources that
should be added to this list. If you have a suggestion please feel free
to email me at richardbyrne (at) freetech4teachers (dot) com.