What is the operation? What is the sign of the integer?

There is so much within the current, common teaching of mathematics that is wrong, yet just accepted that it is correct.  Below, is a link to a letter that I emailed to Cathy Williams, Coordinator, Curriculum and Instruction Unit at the San Diego County Office of Education.  I sent the letter and July 23, 2009 and did not recieve a reply from Cathy.  I will follow up on this some time, soon. The point of the letter is that students are often (almost always) taught operations with integers without having to distinguish between the operation and the sign of the integer.  Often, the symbol for subtraction is magically attached to the ... (read more)

An Introduction to Equations

There are several distinct concepts either introduced or reviewed during this introduction to equations. These are: 1.     balance – expressions on each side of the equal sign are “balanced” or equal 2.     factors and a little bit of multiples, but mostly factors 3.     Fact Families; both for multiplication/division and addition/subtraction 4.     Four operations         related in pairs of inverse operations 5.     the fraction bar used as division 6.     the answer to a ... (read more)

California 6th grade math standard Algebra and Functions (AF) 1.1

AF 1.1:  write and solve one-step linear equations in one variable. The main idea of the Holt (course 1: Number to Algebra; 2008) lessons:  lsn 1-7 through 1-11 is that an unknown amount can be calculated by “undoing” an operation.  So, we should talk about the 4 basic operations and the inverse of each operation.  For multiplication and division, we can also show multiplying by a unit fraction is the inverse of multiplying by the denominator, e.g., ½ of 8 = 4; 2 x 4 = 8; 3 x 5 = 15; 1/3 of 15 = 5.  This is also a nice way to make the point that 2/2 = 1; 3/3 = 1; etc. because ½ of 2 = 1 = 2/2; 1/3 of 3 = 1 ... (read more)

summer planning - the beginning

I've spent the last month mulling over some things to emphasize during this next school year (2010-2011) both in the math content as well as behaviorally. First the behavior: 1.  students must work neatly and carefully:  "neatness and completeness" 2.  be a responsible student:      supplies      behavior 3.  A few phrases to say often      "You must be RESPONSIBLE"      "It's on YOU!"      "It is what you make of it." The content: This is a list of four concepts that I think are ... (read more)