Mr. L's Math» Pedagogy

Friday Afternoon Lifesavers – Math Videos from Bill Lombard – ppt

Bill Lombard — Thu, 03 Nov 2011 12:35:08 +0000

Friday Afternoon Lifesavers – Math Videos from Bill Lombard is the PowerPoint presentation I gave at the California Math Council – South section in November, 2011.

Here is the link to download Friday Afternoon Lifesavers – Math Videos from Bill Lombard – ppt.

Algebra Problem Solving with the new Common Core Standards

Bill Lombard — Thu, 03 Nov 2011 12:15:46 +0000

Algebra Problem Solving with the new Common Core Standards is the PowerPoint presentation I gave at the California Math Council – South section in November, 2011.

Here is the link to download Algebra Problem Solving with the new CC Standards – ppt.

How Many Solutions Are There? – Video Part 1, Linear Equations

Bill Lombard — Mon, 11 Apr 2011 01:39:13 +0000

How Many Solutions Are There - Linear Equations

After working with a concept for awhile, students need to be able to think clearly about the process. This series of worksheets and videos concentrate on asking students to determine HOW MANY solutions exist for particular situations.

Student Directions:

For the given questions, circle the number of solutions. Then state clearly how you determined your answer. NOTE: You may refer to the actual solution, but we are looking for the number of correct solutions.

Explain the reasoning you used to determine your answer. You may use diagrams and symbols, but should explain in words how you arrived at the answer.

Click on How Many Solutions Are There – Linear Equations for the printable pdf file.

KenKen Presentations at NCTM 2011 Annual Meeting

Bill Lombard — Fri, 08 Apr 2011 00:59:57 +0000

I’ve asked for the information download link for the conference handouts and other information from the presenters below. I’ll post the link as soon as it is available. I’m glad to see so much interest in this fabulous puzzle.

KenKen is now the main topic at two independent presentations at the National Council of Teachers of Mathematics (NCTM) 2011 Annual Meeting & Exposition in Indianapolis, April 14-16

KenKen: A Logical Marriage between Sudoku and Arithmetic
April 14, 8:00 am – 9:00 am
Sagamore Ballroom 2 (Indiana Convention Center)
Pamela D. Martin & Kathie O. Smart, Instructors of Mathematics, University of Louisiana at Monroe
Description: How the simplicity and effectiveness of KenKen allow young learners to quickly excel, while challenging their logical thinking.

Using KenKen to Enhance Students’ Learning
April 14, 10:30 am – 12:00 pm
Room 124 (Indiana Convention Center)
Harold B. Reiter, Professor of Mathematics, University of North Carolina at Charlotte
Description: Using KenKen with children and teachers. Professor Reiter will talk about his experiences using the puzzle at a camp in Bangalore, India, and at various teachers’ workshops.

Video – Standardized Test Strategy – Factoring Quadratic Polynomials

Bill Lombard — Fri, 01 Apr 2011 18:38:26 +0000

The Factoring Quadratic Polynomials video shares five approaches/techniques I take in class with students when explaining how to do well on standardized tests. I factor five polynomials using these techniques – remember to pause and rewind as you watch – you’re in total control.

Video – Standardized Test Strategy – Working Backwards

Bill Lombard — Mon, 28 Mar 2011 03:01:07 +0000

The Standardized Test Strategy – Working Backwards video shares one approach I take in class with students when explaining how to do well on standardized tests. It’s helpful to have the correct answer as one of the possible answers given on the test. It’s even nicer when you have some strategies to make it even easier to score better!

You can play the video here or find it on my mathvideouniversity channel on youtube: Standardized Test Strategy – Working Backwards

Video – Standardized Test Strategy – Eliminate Impossible Answers

Bill Lombard — Sun, 27 Mar 2011 21:40:11 +0000

The Standardized Test Strategy – Eliminate Impossible Answers video shares the approach I take in class with students when explaining how to do well on standardized tests. There’s a lot of good thinking that can be found in multiple choice tests, and I stress with students that they want to be “smart test-takers” when doing these tests. I don’t give answers here, but point students in the right direction so they don’t make obvious mistakes.

You can play the video here or find it on my mathvideouniversity channel on youtube: Standardized Test Strategy – Eliminate Impossible Answers

Reverse the Math Puzzle Using 2, 3, and 4

Bill Lombard — Tue, 22 Mar 2011 18:59:16 +0000

I’ve just posted a new video at my mathvideouniversity site on youtube called Reverse the Math Puzzle Using 2, 3, and 4. This puzzle uses the numbers 2, 3, and 4, along with standard operational symbols of mathematics to create the numbers 1 – 10.

The reason it’s called Reverse the Math is that the numbers from 1 – 10 are the target numbers, or essentially the answers to problems that must be created; so students and puzzle enthusiasts are given the answers, but must come up with problems that have the answers from 1 – 10.

Not only is this a great puzzle that builds number sense, it also reinforces a great deal of number properties and provides examples of algebra concepts in a fun way. You can find solutions using exponents, factorials, and square roots, and in most cases there are a number of different ways to express numbers using the given “ingredients.” I’ve used this type of puzzle for years, often spending a week on this as warmups or part of homework. Each day I change the ingredients and watch students’ number sense and enthusiasm grow.

George Polya, Master Problem Solver – a Model for All Math Teachers

Bill Lombard — Tue, 27 Oct 2009 08:20:31 +0000

George Polya

George Polya was a master of problem solving, and his effect on other teachers has been extraordinary. His most popular book, How to Solve It, has sold over a million copies. As is the case with many great books, Polya had been turned down by three publishers before finding one to publish the English version in the United States. It has also been translated into 17 languages. I remember reading this book as a high school student and thinking “What a great writer Mr. Polya is, how clearly he presents his topic: Problem Solving.” His approach has had a lasting impression on the way I teach; I treasure the opportunity of giving other students the joy of discovery and the thrill and satisfaction of solving a problem.

How to Solve It

Polya’s gift was in describing the methods used in solving problems. But he went further; to show teachers how problem solving could be taught and learned. He authored four books on this topic:

How to Solve It
Mathematical Discovery
Mathematics and Plausible Reasoning, volume 1
Mathematics and Plausible Reasoning, volume 2

Some quotes by Polya:

“Solving problems is a practical art, like swimming, or skiing, or playing the piano: You can learn it only by imitation and practice.”

“If you wish to learn swimming you have to go into the water and if you wish to become a problem solver you have to solve problems.”

“Teaching is not a science; it is an art. If teaching were a science there would be a best way of teaching and everyone would have to teach like that. Since teaching is not a science, there is great latitude and much possibility for personal differences. … let me tell you what my idea of teaching is. Perhaps the first point, which is widely accepted, is that teaching must be active, or rather active learning . . . the main point in mathematics teaching is to develop the tactics of problem solving.“

“A Great discovery solves a great problem but there is a grain of discovery in the solution of any problem. Your problem may be modest; but if it challenges your curiosity and brings into play your inventive faculties, and if you solve it by your own means, you may experience the tension and enjoy the triumph of discovery.”

Combo Class Crushes California Competition

Bill Lombard — Sun, 23 Aug 2009 17:53:30 +0000

The California Standardized Testing and Reporting (STAR) Test results have been posted. The Combo classes at Foothill High School have raised the achievement bar once again. Statewide in California at the freshman level, 2% of students taking the STAR test in Algebra 1 score at the Advanced Level.

Three years ago 52% of FHS 9th grade Combo students scored Advanced.

Two years ago 70% of FHS 9th grade Combo students scored Advanced.

Last year 83% of my FHS 9th grade Combo students scored Advanced.

Congratulations, students, for doing such an excellent job. Credit is also due to your parents and your former teachers as well.

People ask frequently at workshops how to achieve such high scores. Here’s what I tell them:

1- Start early – this allows you to use conceptual layering to its maximum benefit. Students benefit from a highly structured, integrated, and conceptually sequenced set of lessons.

2- The STAR test is composed of 25 Algebra 1 Standards. In Mr. L’s class students begin preparing for the STAR test as soon as school begins in August. Since there are about roughly 150 teaching days before the STAR Test, this allows about six days per Standard.

3- Some Standards take more time than others to successfully cover, and many Standards can be taught at the same time. I begin the year with Standards 6, 7, 8, and 9 which cover linear equations. These form a Cluster and can be taught concurrently, thus taking less time than if taught separately. I find that Standards 1 – 5 can be taught throughout the course as we progress through the Algebra 1 curriculum.

4- Rule of 3: Most concepts/skills/algorithms take at least three exposures for students to master. Students need repetition to successfully retain the content. Some algorithms take longer to master, such as the Derivation of the Quadratic Formula. We normally take seven class days to achieve mastery of this skill.

5- Accountability: My students are given frequent short quizzes designed to exhibit total mastery of a skill/concept. This type of skills assessment leads to automaticity – I want students to KNOW how to do things, not just for the short term, but for the long term. They are given the same/similar quizzes throughout the year to maintain their skills.

6- I make STAR prep part of the daily routine with warmups, quizzes, homework, PowerPoint presentations, E-Z writes, and projects.

This high level of performance is due to commitment by Mr. L, parents, students, and former teachers. Students need to:

Commit to time and effort
Commit to Mr. L and their parents
Commit to themselves to do their very best

Any teacher can improve the STAR test scores of students with attention to details. The items above work for my students, and I’m sure they will help your students as well. Best wishes as you work with your students!