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Email Mark V.

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Since being awarded an M.Ed in Secondary Mathematics 2004 and an MS in Mathematics 2006, I have taught sections of Statistics (some with a lab using Excel), Pre-Calc, Trigonometry, developmental Algebra, Algebra II, Contemporary Math I and II. These sections are all taught at the community college level. For the developmental level of algebra I have used CoursesCompasses, MyMathLab and WebAssign in my instruction. I’ve also used many web sites to supplement my lectures.

I embrace the use of technology to aid in instruction. I’ve used Geometer Sketchpad for discovery of area of trapezoids, circumference of circles, arc-length & arc-angles and relations of parallel lines. I used Microsoft Excel for discovery of the general form of the area of pyramids and cones and in Statistics I assigned a project to compare two data bases using mean, variance, standard deviation, CVAR, grouped data and charts. I’ve used SmartView, an TI-83 and TI-84 Graphing calculator emulator, for introducing the coordinate plane, linear equations & relations and measures of variations including Box-and-Whisker plots. I’ve used manipulatives, including algebra tiles and ones I created for demonstrating the properties of parallel lines, finding equations from patterns and multiplication of polynomials.

To stay current, I’ve attend several seminars and workshops. The seminars are given by people involved with Focus on Mathematics and PROMYS (Program in Mathematics for Young Scientists) which stresses habits of the mind. The other seminars were given by the Northeast Sustainable Energy Association (green energy goes to school), Texas Instruments in the use of their graphing calculators, including downloadable instruction, and ETS at AP Statistics reading of the AP Exams.

Corporate Training:

Homeschool:

Science:

Physical Science, Physics

Math:

ACT Math, Algebra 1, Algebra 2, Geometry, Prealgebra, Precalculus, Probability, SAT Math, Statistics, Trigonometry

I've been trained to be a SAT tutor. Like the SAT, the ACT is another college entrance exam. I've taught all subjects covered by the math portion of the SAT.

Algebra:

I've taught several sections of high school algebra at the Community College level. I've also taught algebra as a long term substitute and the high school level. My instruction included the following topics: polynomial arithmetic, introduction to functions, factoring, equations involving absolute values, inequalities and interval notation, factoring sums or differences of cubes, roots and radicals, rational expressions and equations, radical expressions and equations, absolute value inequalities, quadratic equations and the quadratic formula, graphing the equations and inequalities, and solving applied problems.

Geometry:

I've taught several classes of geometry at the high school level. I've used the TI-84 graphing calculator to explore the relation of m and b in the equation y = mx + b and its graph. I've used Excel to model the solids to derive their volume. I also used Excel to show that the area and perimeter of a regular polygon approaches the area and circumference of a circle as n (number of sides) approaches infinity. I've built on these results to show that the volume of a pyramid approaches a cone as n approaches infinity. I've used tables to show the relation between numbers of sides to the sum of interior and exterior angles. I've used tables to show the relation between the number on edges, vertices and surfaces. I've used Geometer Sketchpad to explore geometric shapes including similarity and congruency. I've used Geometer Sketchpad to explore central angles, inscribed angles and arcs.

Algebra 2:

I've taught several sections of College Algebra 2 at the Community College level. I've also taught algebra 2 as a long term substitute and the high school level. My instruction included the following topics:

Linear Equations: solve linear equations;

Linear Inequalities and Absolute Values:

Graphing and Functions:

Systems of Linear Equations:

Exponents, Polynomials and Polynomial Functions:

Factoring: remove the greatest common factor:

Rational Expressions and Functions:

Roots, Radicals and Root Functions:

Quadratic Equations, Inequalities and functions:

Inverse, Exponential and Logarithmic Functions:

Trigonometry:

I've taught several sections of Trigonometry at the Community College level. I've also taught Trigonometry as a long term substitute and at the high school level. My instruction focuses on the unit circle. My instruction included the following topics:

Use and apply radian measure.

Find the values of trigonometric functions of any angle.

Apply trigonometric functions to problem situations involving right triangles

Solve oblique triangles by the laws of sines and cosines.

Graph and interpret sine and cosine curves.

Graph tangent, cotangent, secant and cosecant curves.

Perform vector operations and apply these to problem solving.

Verify trigonometric identities.

Use and apply sum, difference and cofunction identities.

Use and apply double and half- angle identities.

Statistics:

The Nature of Probability and Statistics: Descriptive and Inferential Statistics, Variables and Types of Data, Data Collection and Sampling Techniques, Observational and Experimental Statistics, Uses and Misuses of Statistics, Computers and Calculators.

Frequency Distributions and Graphs: Organizing Data, Histograms, Frequency Polygons, Ogives, Pareto, Time Series Graphs, Pie Charts, Misleading Graphs, Stem and Leaf Plots.

Data Description: Measures of Central Tendency, Mean, Median, Mode, Midrange, Weighted Mean and Distribution Shapes, Measures of Variation, Range, Variance, Standard Deviation for Population and sampling.

Probability and Counting Rules:

Discrete Probability Distributions:

The Normal Distribution:

Confidence Intervals and Sample Size:

Hypothesis Testing: Z and T test for the Mean, z Test for Proportion.

Correlation and Regression:

Test two variables for independence using chi-square.

In the past 6 years I have taught several sections of high school algebra at the Community College level. I've also taught algebra as a long term substitute and the high school level. My instruction included the following topics: polynomial arithmetic, introduction to functions, factoring, equations involving absolute values, inequalities and interval notation, factoring sums or differences of cubes, roots and radicals, rational expressions and equations, radical expressions and equations, absolute value inequalities, quadratic equations and the quadratic formula, graphing the equations and inequalities, and solving applied problems.

In the past 6 years I have taught several sections of College Algebra (Algebra 2) at the Community College level. I've also taught algebra 2 as a long term substitute and the high school level. My instruction included the following topics:

Linear Equations: solve linear equations; solve literal equations

Linear Inequalities and Absolute Values: solve linear inequalities with and without absolute values

Graphing and Functions: graph linear equations and linear inequalities on the rectangular coordinate system; find the slope of a line; write equations given point and slope or two points; work with functions and their applications.

Systems of Linear Equations: solve systems of linear equations in 2 and 3 variables using substitution, elimination and matrix methods.

Exponents, Polynomials and Polynomial Functions: Simplify exponential expressions; add, subtract, multiply and divide polynomials; write a number in scientific notation; multiply and divide numbers written in scientific notation.

Factoring: remove the greatest common factor: factor by grouping; factor trinomials; factor binomials; solve equations and applications by factoring.

Rational Expressions and Functions: Simplify rational expressions; add, subtract, multiply, divide rational expressions; solve applications involving rational expressions.

Roots, Radicals and Root Functions: radical expressions, rational exponents, simplify, solving, adding, subtracting, multiplying and dividing radical expressions, using complex numbers.

Quadratic Equations, Inequalities and functions: Solve and graph a quadratic equation using factoring, square root property, completing the square and quadratic formula, solve application problems.

Inverse, Exponential and Logarithmic Functions: inverse functions, exponential functions, properties of common and natural logarithmic functions.

I've been trained to be a SAT tutor. I've taught all subjects covered by the math portion of the ASVAB. I'm certified to teach General Science by the state of Mass., I'm an avid reader, I was a flight simulator tech in the Air Force (electronics and computers). I worked in the mobile simulator program where I was required to work on generators, hydraulic systems, heating and air conditioning systems. I also own, maintain and modify an electric automobile build in 1992. I've also designed and programmed robotic systems.

I've taught several classes of geometry at the high school level. I've used the TI-84 graphing calculator to explore the relation of m and b in the equation y = mx + b and its graph. I've used Excel to model the solids to derive their volume. I also used Excel to show that the area and parameter of a regular polygon approaches the area and circumference of a circle as n (number of sides) approaches infinity. I've built on these results to show that the volume of a pyramid approaches a cone as n approaches infinity. I've used tables to show the relation between numbers of sides to the sum of interior and exterior angles. I've used tables to show the relation between the number on edges, vertices and surfaces. I've used Geometer Sketchpad to explore geometric shapes including similarity and congruency. I've used Geometer Sketchpad to explore central angles, inscribed angles and arcs.

In the past 6 years I have taught several sections of high school algebra at the Community College level. I've also taught algebra as a long term substitute and the high school level. Most lessons include review of mathematics topics taught in middle school. I'm licensed by the state of MA in secondary mathematics grades 7 - 12.

Precalculus (Trigonometry)

In the past 7 years I have taught several sections of Algebra 2, Trigonometry and Precalculus at the Community College level. I've also taught Algebra 2 and Trigonometry as a long term substitute and the high school level. My instruction included the following topics:

1. use and apply radian measure.

2. find the values of trigonometric functions of any angle.

3. apply trigonometric functions to problem situations involving right triangles

4. solve oblique triangles by the laws of sines and cosines.

5. graph and interpret sine and cosine curves.

6. graph tangent, cotangent, secant and cosecant curves.

7. perform vector operations and apply these to problem solving.

8. verify trigonometric identities.

9. use and apply sum, difference and cofunction identities.

10. use and apply double and half- angle identities.

11. Also the use of the TI-84 calculator

From Algebra 2:

12. Linear Equations: solve linear equations;

13. Linear Inequalities and Absolute Values:

14. Graphing and Functions:

15. Systems of Linear Equations:

16. Exponents, Polynomials and Polynomial Functions:

17. Factoring: remove the greatest common factor:

18. Rational Expressions and Functions:

19. Roots, Radicals and Root Functions:

20. Quadratic Equations, Inequalities and functions:

21. Inverse, Exponential and Logarithmic Functions:

From College Precalculus:

22. work with complex numbers in rectangular, polar and exponential forms.

23. find inverse functions and the composition of functions.

24. use the remainder theorem and factor theorem.

25. solve and graph polynomial, rational, exponential and logarithmic functions both with and without the use of a calculator.

26. determine and graph the conic sections.

27. apply the knowledge of mathematical concepts to problem solving

27. apply skills to several optional topics such as sequences, series, mathematical induction, limits, matrix solutions to systems of linear and nonlinear equations and inequalities.

I've been trained to be a SAT tutor. I've taught all subjects covered by the math portion of the SAT.

Algebra:

I've taught several sections of high school algebra at the Community College level. I've also taught algebra as a long term substitute and the high school level. My instruction included the following topics: polynomial arithmetic, introduction to functions, factoring, equations involving absolute values, inequalities and interval notation, factoring sums or differences of cubes, roots and radicals, rational expressions and equations, radical expressions and equations, absolute value inequalities, quadratic equations and the quadratic formula, graphing the equations and inequalities, and solving applied problems.

Geometry:

I've taught several classes of geometry at the high school level. I've used the TI-84 graphing calculator to explore the relation of m and b in the equation y = mx + b and its graph. I've used excel to model the solids to derive their volume. I also used excel to show that the area and parameter of a regular polygon approaches the area and circumference of a circle as n (number of sides) approaches infinity. I've built on these results to show that the volume of a pyramid approaches a cone as n approaches infinity. I've used tables to show the relation between numbers of sides to the sum of interior and exterior angles. I've used tables to show the relation between the number on edges, vertices and surfaces. I've used Geometer Sketchpad to explore geometric shapes including similarity and congruency. I've used Geometer Sketchpad to explore central angles, inscribed angles and arcs.

Algebra 2:

I've taught several sections of College Algebra 2 at the Community College level. I've also taught algebra 2 as a long term substitute and the high school level. My instruction included the following topics:

Linear Equations: solve linear equations;

Linear Inequalities and Absolute Values:

Graphing and Functions:

Systems of Linear Equations:

Exponents, Polynomials and Polynomial Functions:

Factoring: remove the greatest common factor:

Rational Expressions and Functions:

Roots, Radicals and Root Functions:

Quadratic Equations, Inequalities and functions:

Inverse, Exponential and Logarithmic Functions:

Trigonometry:

I've taught several sections of Trigonometry at the Community College level. I've also taught Trigonometry as a long term substitute and the high school level. My instruction focuses on the unit circle. My instruction included the following topics:

Use and apply radian measure.

Find the values of trigonometric functions of any angle.

Apply trigonometric functions to problem situations involving right triangles

Solve oblique triangles by the laws of sines and cosines.

Graph and interpret sine and cosine curves.

Graph tangent, cotangent, secant and cosecant curves.

Perform vector operations and apply these to problem solving.

Verify trigonometric identities.

Use and apply sum, difference and cofunction identities.

Use and apply double and half- angle identities.

Statistics:

The Nature of Probability and Statistics: Descriptive and Inferential Statistics, Variables and Types of Data, Data Collection and Sampling Techniques, Observational and Experimental Statistics, Uses and Misuses of Statistics, Computers and Calculators.

Frequency Distributions and Graphs: Organizing Data, Histograms, Frequency Polygons, Ogives, Pareto, Time Series Graphs, Pie Charts, Misleading Graphs, Stem and Leaf Plots.

Data Description: Measures of Central Tendency, Mean, Median, Mode, Midrange, Weighted Mean and Distribution Shapes, Measures of Variation, Range, Variance, Standard Deviation for Population and sampling.

Probability and Counting Rules:

Discrete Probability Distributions:

The Normal Distribution:

Confidence Intervals and Sample Size:

Hypothesis Testing: Z and T test for the Mean, z Test for Proportion.

Correlation and Regression:

Test two variables for independence using chi-square.

In the past 6 years I have taught more than a dozen sections of Elementary Statistics at the Community College level. These courses included a chapter on probability and counting. I have been an AP Statistics reader since 2011. A reader corrects the open response questions. I also used statistics as a manufacturing engineer at Raytheon and software engineer at GCA. My instruction included the following topics:

The Nature of Probability and Statistics: Descriptive and Inferential Statistics, Variables and Types of Data, Data Collection and Sampling Techniques, Observational and Experimental Statistics, Uses and Misuses of Statistics, Computers and Calculators.

Frequency Distributions and Graphs: Organizing Data, Histograms, Frequency Polygons, Ogives, Pareto, Time Series Graphs, Pie Charts, Misleading Graphs, Stem and Leaf Plots.

Data Description: Measures of Central Tendency, Mean, Median, Mode, Midrange, Weighted Mean and Distribution Shapes, Measures of Variation, Range, Variance, Standard Deviation for Population, Samples and Grouped Data, Coefficient of Variation, Range Rule of Thumb, Chebyshev’s Theorem, Empirical Rule, Measure of Position, Standard Scores, Percentiles, Quartiles and Deciles, Outliers.

Probability and Counting Rules: Sample Spaces and Probability, Classical, Empirical and Subjective Probability, Complementary Events, Law of Large Numbers, Probability and Risk Taking, Addition Rules for Probability, Multiplication Rules and Conditional Probability, Counting Rules, Factorials, Permutations and Combinations.

Discrete Probability Distributions: Probability Distributions, Mean, Variance, Standard Deviation and Expectation, Binomial Distributions.

The Normal Distribution: Properties of a Normal Distribution, Standard Normal Distribution, Areas Under Curve and Probabilities, Applications of the Normal Distribution, Central Limit Theorem, Normal Approximation to the Binomial Distribution.

Confidence Intervals and Sample Size: Confidence Intervals for Mean and Sample Size, Confidence Intervals and Sample Size for Proportions, Confidence Intervals for Variance and Standard Deviations, test the difference between means for dependent samples, test the difference between means for two independent samples, test for the difference between two proportions.

Hypothesis Testing: Steps in Hypothesis Testing-Traditional Method, z Test for the mean, t Test for the Mean, z Test for Proportion.

Correlation and Regression: Scatter Plots, Correlation and Regression testing.

Test two variables for independence using chi-square, test a distribution for goodness of fit using chi-square.

In the past 7 years I have taught several sections of Trigonometry at the Community College level. I've also taught Trigonometry as a long term substitute and the high school level. My instruction focuses on the unit circle. My instruction included the following topics:

1. use and apply radian measure.

2. find the values of trigonometric functions of any angle.

3. apply trigonometric functions to problem situations involving right triangles

4. solve oblique triangles by the laws of sines and cosines.

5. graph and interpret sine and cosine curves.

6. graph tangent, cotangent, secant and cosecant curves.

7. perform vector operations and apply these to problem solving.

8. verify trigonometric identities.

9. use and apply sum, difference and cofunction identities.

10. use and apply double and half- angle identities.

11. Also the use of the TI-84 calculator

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