I know that one of the most stressful times for students is test taking days. When you say “math test” you can almost see the terror in the eyes of most of the students. I have spent some time thinking about why that might be. Students read a book in an English class and feel comfortable answering some question. On the other hand, they learn a concept such as graphing lines, and all of a sudden feel like there is no way that they can answer any questions. This fear and anxiety triples as students think about standardized tests such as the AP Exam, SAT, and ACT.
After really thinking about this in my years of teaching I decided that math is a pretty black and white subject. Students either get the question right or wrong and that scares them. They can interpret a book, but either you graphed the line correctly, or you didn’t.
There are a couple of test taking strategies that I have often shared with students.
1. Go through old exams, quizzes and homework.
2. Identify your weak areas and work on those first.
3. Eat a good breakfast the day of the test.
4. RELAX!!!!!!! It is one of many tests you will be taking throughout your life.
5. Glance over the test when you get it and come up with a quick plan.
6. Manage your time. Don’t spend too much time on any one question.
7. Read the questions very carefully. If you don’t understand the directions, ASK!!!
8. If you don’t know a question, then skip it. Do not dwell on it.
9. Did I mention relax!!!!
I also found some good websites to visit with test taking strategies. The following are general test taking strategies for math tests:
Website 1
Website 2
Website 3
Website 4
The following website is geared towards the AP Exam:
AP Test Taking
The following are geared towards the ACT and SAT Exams:
Website 5
Website 6
Website 7
Website 8
See you all next week.
Sunday, March 29, 2009
Sunday, March 22, 2009
Calculus Again
I will be starting a Calculus project in the next couple of weeks and I was thinking what it was like for me to take Calculus back in high school. Internet was just starting and it was not readily available in schools. I had a very old and clunky TI-82 Calculator. I think it may have been the first graphing calculator they made. I think of what the students have available to them now, and I marvel. I know some teachers think that students rely on technology too much, but I think we need to provide students with different options. Of course students should be able to take a derivative, but does it make sense at some point for students to struggle though large derivatives if we are testing another skill?
I looked through the internet to find some helpful sites for students and for teachers.
The first is a complete Calculus class on Hippocampus.org. There is also a Spanish version of the course which is wonderful. Math is supposed to be the universal language so it is wonderful that language is not a barrier in this case.
I also found a wonderful website with an extensive list of graphics that can be used by students and teachers.
Cow.math offers a list of small calculus modules. These modules can be used by students as extra practice or students can use them for remediation purposes.
I also looked for websites to help students with their TI-83 calculators. The website prenhall.com has an incredible table of contents for every TI-83 calculator that has been made.
For those students that are interested in the history behind Calculus, I found a great website that outlines how we came to be studying this subject.
As always, please share your finds with the rest of us and see you next week.
I looked through the internet to find some helpful sites for students and for teachers.
The first is a complete Calculus class on Hippocampus.org. There is also a Spanish version of the course which is wonderful. Math is supposed to be the universal language so it is wonderful that language is not a barrier in this case.
I also found a wonderful website with an extensive list of graphics that can be used by students and teachers.
Cow.math offers a list of small calculus modules. These modules can be used by students as extra practice or students can use them for remediation purposes.
I also looked for websites to help students with their TI-83 calculators. The website prenhall.com has an incredible table of contents for every TI-83 calculator that has been made.
For those students that are interested in the history behind Calculus, I found a great website that outlines how we came to be studying this subject.
As always, please share your finds with the rest of us and see you next week.
Sunday, March 15, 2009
Graphing Linear Functions
Just recently I was working with a student on graphing linear functions during a tutoring session. She asked if there was anything she could work on to continue with her practice. This prompted me to get on the computer and do a search for some lessons and interactives that might help her.
I started my search with Hippocampus.org. The full Algebra 1 class has an entire chapter devoted to graphing linear functions. This is a wonderful place for students to start if they are having trouble with the concept or need a refresher.
I also came across some great interactives that can really help students. The first is an online graphing utility that I have used in the past called GCalc. This will allow students the ability to graph any function, including linear functions.
The second is a Shodor Interactive that will also allow students to graph linear functions. You may ask why give students an opportunity to graph functions with technology instead of with paper and pencil methods. I am a huge proponent of doing both. Students need to know the mechanics of graphing functions on their own, but we should also expose students to the technology that is available to them.
I also found two sliding interactives. Students are able to move a slide that changes the slope and y-intercept of an equation and they can see how these changes affect the graph of a linear function. One of these interactives can be found at mathsnet and the other at id.mind.
Finally, I found a site that offers free graph paper. I think that is also important when students are practicing these skills.
I started my search with Hippocampus.org. The full Algebra 1 class has an entire chapter devoted to graphing linear functions. This is a wonderful place for students to start if they are having trouble with the concept or need a refresher.
I also came across some great interactives that can really help students. The first is an online graphing utility that I have used in the past called GCalc. This will allow students the ability to graph any function, including linear functions.
The second is a Shodor Interactive that will also allow students to graph linear functions. You may ask why give students an opportunity to graph functions with technology instead of with paper and pencil methods. I am a huge proponent of doing both. Students need to know the mechanics of graphing functions on their own, but we should also expose students to the technology that is available to them.
I also found two sliding interactives. Students are able to move a slide that changes the slope and y-intercept of an equation and they can see how these changes affect the graph of a linear function. One of these interactives can be found at mathsnet and the other at id.mind.
Finally, I found a site that offers free graph paper. I think that is also important when students are practicing these skills.
Monday, March 9, 2009
Geometric Proofs
I believe hands down the toughest subject for students is proofs. There are a few reasons why that is the case. Number one, proofs tend to be taught very early in a geometry course. There is no way around it, but it causes students some problems. You have to teach proofs in order to work with theorems in a Geometry course, yet you teach proofs before students know a lot of definitions, postulates and theorems. The subject seems to come out of nowhere for students and causes some stress.
I want to give everyone a few websites that students can refer too while working with proofs. Hopefully this extra information will help students transition their thinking from Algebra to Geometry and especially geometric proofs.
Sparknotes have a great set of pages that can really help students. The website includes a table of contents that is very thorough.
Proofs for Dummies is another good website that seems to be affiliated with the popular books.
Another great website is How to Write Proofs. Again, there is a comprehensive table of contents that includes direct proof, proof by contradiction, counterexamples, just to name a few.
The Library of Math has a huge collection of proofs that students can use as a reference. Sometimes students need a few examples to see how proofs are constructed.
If anyone has any other websites to share I would love to see them. I have written and taught Geometry and this is always a difficult subject for me to explain to students well. Share your experiences in the classroom as well. I know I will learn a lot.
I want to give everyone a few websites that students can refer too while working with proofs. Hopefully this extra information will help students transition their thinking from Algebra to Geometry and especially geometric proofs.
Sparknotes have a great set of pages that can really help students. The website includes a table of contents that is very thorough.
Proofs for Dummies is another good website that seems to be affiliated with the popular books.
Another great website is How to Write Proofs. Again, there is a comprehensive table of contents that includes direct proof, proof by contradiction, counterexamples, just to name a few.
The Library of Math has a huge collection of proofs that students can use as a reference. Sometimes students need a few examples to see how proofs are constructed.
If anyone has any other websites to share I would love to see them. I have written and taught Geometry and this is always a difficult subject for me to explain to students well. Share your experiences in the classroom as well. I know I will learn a lot.
Tuesday, March 3, 2009
Matrix Multiplication and Solving Systems of Equations
Last week we talked about the basic operations of matrices and how to find a matrix inverse. This week we will continue to our discussion of matrices by talking about matrix multiplication and solving systems of equations using matrices.
I recommend starting the discussion by talking about when matrix multiplication can occur. Remember that if two matrices can be multiplied, their inner dimensions are the same. For example, if matrix A has dimensions 2 x 4 and matrix B has dimensions 4 x 5 then the matrices can be multiplied since the inner dimensions of 4 are the same. The product matrix will have dimensions 2 x 5. It is important to start with this fact so that students do not spend time working on problems that can’t be completed.
The following are some helpful websites that I found that can help students and teachers work through the concept of matrix multiplication.
The Math Warehouse website has a great step by step explanation of matrix multiplication. There are great tutorials as well that take students through the entire process.
Most graphing calculators will do matrix multiplication for students but we can’t expect all students to be able to own or use a graphing calculator. There are some great online calculators such as the Easy Calculations Calculator and the Analyze Math Applet. Students can use these sites to check their work.
Solving systems of equations is also a concept that utilizes matrices, especially when working with three equations and three unknowns. Matrices are the easiest way to solve these types of problems. Spark Notes and Cliff Notes both have great summaries of how matrices can be used to solve systems of equations. I also found a great tutorial on how to use graphing calculators to solve systems of equations using matrices.
As always, please share your finds with the rest of the readers. Next week we will talk more closely about proofs.
I recommend starting the discussion by talking about when matrix multiplication can occur. Remember that if two matrices can be multiplied, their inner dimensions are the same. For example, if matrix A has dimensions 2 x 4 and matrix B has dimensions 4 x 5 then the matrices can be multiplied since the inner dimensions of 4 are the same. The product matrix will have dimensions 2 x 5. It is important to start with this fact so that students do not spend time working on problems that can’t be completed.
The following are some helpful websites that I found that can help students and teachers work through the concept of matrix multiplication.
The Math Warehouse website has a great step by step explanation of matrix multiplication. There are great tutorials as well that take students through the entire process.
Most graphing calculators will do matrix multiplication for students but we can’t expect all students to be able to own or use a graphing calculator. There are some great online calculators such as the Easy Calculations Calculator and the Analyze Math Applet. Students can use these sites to check their work.
Solving systems of equations is also a concept that utilizes matrices, especially when working with three equations and three unknowns. Matrices are the easiest way to solve these types of problems. Spark Notes and Cliff Notes both have great summaries of how matrices can be used to solve systems of equations. I also found a great tutorial on how to use graphing calculators to solve systems of equations using matrices.
As always, please share your finds with the rest of the readers. Next week we will talk more closely about proofs.
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