Math Anxiety

Anxiety is a basic human emotion consisting of fear and uncertainty that typically appears when an individual perceives an event as being a threat to the ego or self-esteem (Sarason, 1988).  Everyone gets anxious sometime about one thing or another, how we deal with that anxiety is a different matter. Things are said or done incorrectly when someone is anxious. As teachers our first day or even the first week of school is very important. Here is when students have an opportunity to assess our style of teaching and our chemistry to see if it is a good fit. We the teachers are doing pretty much the same with the students.

Anxiety is relaxed or turned off when students are made to feel comfortable. When students feel that their interest is met and they are challenged. When they realize that the teacher is also human. An educator one asked the students on the first day of class “Are you nervous?”  The response was “Yes”.  He replied, “So am I”.  Everyone had a good laugh and the tension was broken. Once students know that you feel as they feel and that you have their best interest, there will be flow.

Knowing our students and subject matter are key to anxiety reduction. We must be able to see the blank or confused looks and adjust our lesson to meet the students need. When we are prepared and are familiar with our subject we can begin to differentiate at that time to alleviate anxiety for those who seem to be lost or bored. Anxiety is reduced when both students and teachers know what is to be expected. Student also knows that part of this process is testing. How we plan, teach and execute our assessment would also ease the tension of the students.

Most people would not be against a surprise birthday party. However, a surprise test is entirely a different issue. Students not only want to know that a test is coming, but what is on the test, what is the format of the test and how it will be graded. If the teacher has laid a good foundation by engaging the students, giving positive feedback and having some fun, then the anxiety level towards assessments becomes next to nil.  

Most of us wrote our required lesson plans for the course and they were wonderful, excellent and I’m sure stimulating.  The practicality of the matter is that some students may not care, some students may not know how to start the assignment, some students may be low readers and just don’t understand. Our responsible is to encourage by building up their self-esteem and confidence. When a student knows that a teacher has confidence in them, the students go the extra mile to show that they are worthy of that praise. Anxiety – what’s that?

http://www.ericdigests.org/2005-2/anxiety.html

See full size image

http://www.mathgoodies.com/articles/math_anxiety_model.html

Look up, out, and beyond.  Math helps answer big questions, not just mundane ones. 

Let the spirit of inquiry be a comfortable and joyous one – not a chore! 

It’s okay to let them struggle to find their own answers, their own way, in their own time. It’s important for children to feel  comfortable with hard questions, and not to feel the need for fast answers. 

http://www.google.com/imgres?imgurl=http://www.suzannesutton.com/_borders/rain.gif&imgrefurl=http://www.suzannesutton.com/k-3.htm&usg=__Km0AcJwj-S6KNZtr9ZZ4rKJUEOk=&h=1751&w=1152&sz=60&hl=en&start=19&zoom=1&um=1&itbs=1&tbnid=_4tbIYUgJDEEuM:&tbnh=150&tbnw=99&prev=/images%3Fq%3Dmath%2Banxiety%26um%3D1%26hl%3Den%26sa%3DX%26rlz%3D1T4ADSA_enUS348US349%26tbs%3Disch:1

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Wolfram Mathematica

I watched the on demand presentation of an Overview of Mathematica for education by Cliff Hastings and was very impressed. It was dynamic knowing that there are tools such as this to enhance teaching and learning. The presentation was very informative.  I was amazed at the inactive manipulations that took place.

Hastings gave the three rules that must be followed in doing various calculations. He also demonstrated the way a function could be manipulated to allow for ‘what if ‘ scenarios. Not only does the system give solution to problems, but it also explains the concept, if needed. What was shown and explained is only the top of the iceberg.  There are several topics that are covered by Mathematica, including information on other subject.  The attached link would be able to get you started

http://www.wolfram.com/broadcast/seminars/s01/

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Math textbook Engaging or Discouraging?

My analysis was based on the text GEOMETRY by Isidore Dressler. This book is not user friendly, or rather student friendly. It has the traditional approach. It requires a lot of memorization and drills in the form of exercises to ensure learning takes place. I could select any chapter and it is all about Math drills-no deviation. Students are just required to learn as outlined – no relevance to their background or future.

The following is what Chapter III looks like. It deals with Congruent Triangles and it is focused on skills.

A student has to go through all those pages of agony in order to understand congruent triangles. It looks like so many words to read. Is it necessary? Devlin stated in his article ‘In Math you have to Remember….’ That mathematics is a way of thinking about problems and issues in the world. Get the thinking right and the skills come largely for free.’     In this text you have to get the skills first-memorize.  Where do I start to decode to make this chapter user-friendly and not have students zone out on me.

This text fits into Bloom’s lower level task with knowledge (remember and memorize). It also covers application, in using the formulas to apply to the exercises at the end of the chapter. However, there is no stimulation, creativity and higher-order critical thinking. The text did it all for the student. Other sources would have to be utilized in order to bring this lesson to life.

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Thinking vs remembering

Comments based on article from Devlin’s Angle-In math you Have to Remember……. and Gas station without pumps file under uncategorized.

Mathematics came about because man (mankind) wanted a better and more efficient way of doing things. The Inca Empire used the Quipu (knotted ropes using a positional decimal system). This was use for crops, taxes, population and many other data. The Egyptians used the Pythagorean Theorem for construction, architecture and measurement. These methods weren’t about remembering but about critical-thinking and action. Somewhere along the life’s line we lost the true meaning of Mathematics and it became rote. Math became an intellectual sport that didn’t require reasoning, just memorization and application.  We must begin figure out how to get the gas from the gas station. Devlin was right when he said that ‘Mathematics is a way of thinking about problems and issues in the world. Get the thinking right and the skills come largely for free.’ I also agree that we must start with an interesting “hook”.  

http://gasstationwithoutpumps.wordpress.com/2010/07/05/math-isnt-memory-work/

http://www.maa.org/devlin/devlin_06_10.html

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Bloom’s Assessments

Quadratic Equation Lesson

In this lesson of quadratic equation, Bloom’s Taxonomy is seen throughout every step to ensure that the students grasp the concept of the lesson. The lesson is engaging, requires computative skills,  creativity and social networking. Questions are asked to check for knowledge and understanding. Formula is applied for problem solving and creativity. Finally information is shared and evaluated.

Quadratic Equations is Fx² + Ux + N

 Knowledge -Definition – Quadratic equation is an equation in which the highest power of an unknown quantity is a square. It is a polynomial equation of the second degree.

 Knowledge-What does it look like?

A ‘standard’ quadratic equation

                                                ax²  +  b+  c   =  0

 Analysis/Comprehension-Let’s break it down

  • The letters a, b and c are coefficients (you know those values). They can have any value, except that a cannot be 0. [Remember a coefficient is a number before a variable)
  • The letter “x” is the variable (you don’t know the value as yet)
 

Here is an example of one:

Give explanation as to why it is called a quadratic equation when it is only raised to the 2nd power. (Hint: word origination)

 Quadratic equations are called quadratic because quadratus is Latin for “square”; in the leading term the variable is squared. The name Quadratic comes from “Quad” meaning square because the variable is squared (like x²). It is also called an ‘Equation of Degree 2’ because of the 2 on the x.

The solutions to the Quadratic Equation are where it is equal to zero. There are usually 2 solutions to the equation.

They are also called “roots”, or sometimes “zeros”

 There are 3 ways to find the solutions:

1)      You can factor the Quadratic (find what to multiply to make the Quadratic Equation)

2)      You can complete the Square

3)      You can use the Quadratic Formula:          

                             

Remembering: It is read “minus b plus or minus the square root of b-squared minus four ac, all over two a”. It’s like driving a car once you know it, you won’t forget it: it takes you places fast.

Application – The “±” means you need to do a plus AND a minus, and therefore there are normally TWO solutions! You don’t have to choose, I’ll take both.

The blue part (b² – 4ac) is called the “discriminant”, because it can “discriminate” between the possible types of answer.  If it is positive, you will get two normal solutions, if it is zero you get just one solution, and if it is negative you get imaginary solutions.

 Examples of problems would be modeled, solved and graphed. Students would be given exercises to check for comprehension. 

 Synthesis-Students would be asked to create a quadratic problem, explain, graph and solve after reading the origin of the Quadratic Equation. How did this come about? Why do we need it and what would we use it for today?

 Students would be given rubrics to evaluate each other.

The following website would help with origin, further analysis and creativity.

http://plus.maths.org/content/101-uses-quadratic-equation

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Quadratic Equations

Quadratic Equations is Fx² + Ux + N

Definition – Quadratic equation is an equation in which the highest power of an unknown quantity is a square. It is a polynomial equation of the second degree.

What does it look like?

A ‘standard’ quadratic equation

                                                ax²  +  bx  +  c   =  0

Let’s break it down

  • The letters a, b and c are coefficients (you know those values). They can have any value, except that a cannot be 0. [Remember a coefficient is a number before a variable, x is the variable. It is unknown]
  • The letter “x” is the variable (you don’t know the value as yet)
 

Here is an example of one:

Give explanation as to why it is called a quadratic equation when it is only raised to the 2nd power. (Hint: word origination)

The solutions to the Quadratic Equation are where it is equal to zero. There are usually 2 solutions to the equation.

They are also called “roots”, or sometimes “zeros”

There are 3 ways to find the solutions:

1)      You can factor the Quadratic (find what to multiply to make the Quadratic Equation)

2)      You can complete the Square

3)      You can use the Quadratic Formula:

It is read “minus b plus or minus the square root of b-squared minus four ac, all over two a”

The entire formula can now be explained. The following website gives conceptual information in a fun way.

http://www.coolmath.com/algebra/09-solving-quadratics/05-solving-quadratic-equations-formula-02.htm

http://www.geogebra.org/en/wiki/index.php/Quadratic_Equations

Quadratic Rap – would no longer forget formula

http://www.youtube.com/watch?v=p1Jpdkf2HWY&feature=related

Project  and Exercise- use link

http://www.mrbenshoof.com/alg2Documents/Quadratic%20Equations%20Project.pdf

Using the Quadratic Formula solve the following problem

Just put the values of a, b and c into the quadratic Formula and, do the calculations, also graph the equation.

 5x² + 6x+ 1= 0

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Statistics Lesson

This lesson would promote team work, creativity, strategy, learning and fun.

Subjects

  • Algebra
  • Mathematics
    — Simple Graphing
    — Simple Statistics

Grades

  • 8-9

Brief Description

Perplexing Puzzles allows students to work in groups to put a puzzle together. Use this lesson to teaching graphing or the concept of a scatter plot.

Objectives

Students

  • understand the concept of a scatter plot. (Younger students will develop an understanding of simple graphs.)
  • plot points for time and number of puzzle pieces put together.
  • discuss or write about what their graphs show.

Keywords

scatter plot, graph, x axis, y axis, puzzle, jigsaw puzzle

Materials Needed

  • jigsaw puzzles of about 250-500 pieces, one puzzle per group of 4 students; puzzles should be of same level of difficulty for all groups (very difficult puzzles are fine)
  • stopwatch (optional)

The Lesson

Arrange students into groups of 4. Provide each group with a jigsaw puzzle of similar difficulty. The puzzles might be between 250 and 500 pieces. Extra difficult puzzles are fine.

Give student groups about 5 minutes to organize their puzzle pieces. In this time, they should turn over all the pieces so the picture sides are up, and they can begin to separate outside-edge pieces from inner pieces.

Provide a class period for groups of students to work on putting together their puzzles. Set a stopwatch for 5-minute intervals. At each interval, ask students to record the number of puzzle pieces put together during the previous 5 minutes. (Note: Groups may not finish the entire puzzle in the class period, but that is fine.)

Allow students to work on the puzzle for a full class period. The next class period (or as homework), have students create graphs to show the number of puzzle pieces put together by the students in their group for each 5-minute interval.

  • Young students might create bar graphs. Each bar will illustrate the number of pieces put together in a different 5-minute interval.
  • Older students will create scatter-plot graphs. They will mark the x axis of their graphs “Time” and the y axis “Number of Puzzle Pieces Put Together” and plot the points on the graph.

Assessment

Have students use their completed graphs to write an explanation of what the graphs show. In their writing students should explain the relationship between time and the number of puzzle pieces put together. They might answer questions such as

  • Why does the graph look the way it does?
  • What variables affected the number of pieces put together at different intervals?
  • Based on the collected data, how much time do they estimate it would take the group to complete the entire puzzle?
  • What was your group’s strategy for putting the pieces together?
  • Was your group successful at completing the puzzle? Why or why not?

As a culminating activity, students might complete their puzzles and put puzzle glue on them. Once dry, the puzzles could be attached to classroom ceiling tiles as decoration

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