tag:blogger.com,1999:blog-18594064971590480602011-10-25T06:05:37.653-07:00A Math Teacher who Writes (or a Writer who DOES MATH). Charles Bukowski said: "I write because I don't know what I think until I read what I say" Seems like a perfectly fine rationale to me.ERKOhttp://www.blogger.com/profile/01453699893902804035noreply@blogger.comBlogger5801100tag:blogger.com,1999:blog-1859406497159048060.post-84641597147616717952011-06-02T09:09:00.001-07:002011-06-02T09:10:17.642-07:00

As an Instruction Math Coach, I am considering the themes of math instruction with my cohort of teachers. Content knowledge Understanding network of connections Disposition towards mathematics Personal feelings about math Pedagogical content knowledge Developing and maintaining learning communities Knowing how to “unpack” big math ideas Underlying beliefs about learning Teaching styles

ERKOhttp://www.blogger.com/profile/01453699893902804035noreply@blogger.com0tag:blogger.com,1999:blog-1859406497159048060.post-39789326474402402072011-06-02T08:32:00.001-07:002011-06-02T08:32:44.307-07:00

With the possible exception of the equator, everything begins somewhere.   C.S. Lewis

ERKOhttp://www.blogger.com/profile/01453699893902804035noreply@blogger.com0tag:blogger.com,1999:blog-1859406497159048060.post-56168777755148907722011-06-02T08:31:00.001-07:002011-06-02T08:31:21.622-07:00

Today I begin a new phase as Math Instructional Coach. This is an observation protocol I am working on: What is the evidence that important mathematics is at the core of the lesson?Teacher has clear summary of lesson Teacher can respond to unexpected student questions Discern between important math concepts and tangential ones What is the nature of the interactions between teacher and

ERKOhttp://www.blogger.com/profile/01453699893902804035noreply@blogger.com0tag:blogger.com,1999:blog-1859406497159048060.post-91751380420080014432011-05-27T08:22:00.001-07:002011-05-27T08:22:41.635-07:00

Change is Nature's delight.  Marcus Aurelius

ERKOhttp://www.blogger.com/profile/01453699893902804035noreply@blogger.com0tag:blogger.com,1999:blog-1859406497159048060.post-65685855888362554172011-05-26T21:43:00.000-07:002011-05-26T21:46:02.675-07:00

My students have all been clamoring for a "party". They expect me to buy pizza, they bring chips and soda. Classroom parties are just big food fests. So many of my students are really quite overweight. If I were to buy them pizza, they would eat it in class and still go to lunch and eat the horrendous food there. I will NOT be buying pizza, nor allowing the chips and sodas in my room. I

ERKOhttp://www.blogger.com/profile/01453699893902804035noreply@blogger.com1tag:blogger.com,1999:blog-1859406497159048060.post-46173348074651885932011-05-26T21:11:00.000-07:002011-05-26T21:13:12.579-07:00

Digging around I find that there are no hard, cold facts readily available about the cost of the Iraq war. Depending on political bent and accounting practices, the numbers range from the billions to more than 3 trillion. I found this table, which broke down the numbers in an interesting fashion: It got me thinking that the average teacher's salary would be covered in less than 20 seconds.

ERKOhttp://www.blogger.com/profile/01453699893902804035noreply@blogger.com0tag:blogger.com,1999:blog-1859406497159048060.post-57808199783321650312011-05-26T20:59:00.000-07:002011-05-26T20:59:46.273-07:00

I was looking around the Internet to see the status of Common Core Standards in California. I found the excerpt below, indicating that they have been adopted but have run against a moratorium of funding for new framework initiatives. Part of me really understands this moratorium because it has felt that we have been buffeted around with new initiatives ever 3-4 years. I am not convinced we need

ERKOhttp://www.blogger.com/profile/01453699893902804035noreply@blogger.com0tag:blogger.com,1999:blog-1859406497159048060.post-12542926575611674372011-05-26T14:09:00.000-07:002011-05-26T14:11:31.356-07:00

What are educational standards?Educational standards help teachers ensure their students have the skills and knowledge they need to be successful by providing clear goals for student learning.Why do we need educational standards?We need standards to ensure that all students, no matter where they live, are prepared for success in postsecondary education and the workforce. Common standards will

ERKOhttp://www.blogger.com/profile/01453699893902804035noreply@blogger.com0tag:blogger.com,1999:blog-1859406497159048060.post-88592858835907311972011-05-25T23:09:00.000-07:002011-05-25T23:09:07.717-07:00

There are three main pillars upon with 5th grade math learning rests: 1. Fractions 2. Division 3. 3 dimensional shapes and their measurement Here is what the Common Core Mathematics Standards have to say: Students apply their understanding of fractions and fraction models to represent the addition and subtraction of fractions with unlike denominators as equivalent calculations with like

ERKOhttp://www.blogger.com/profile/01453699893902804035noreply@blogger.com2tag:blogger.com,1999:blog-1859406497159048060.post-2468779750563964132011-05-25T22:16:00.000-07:002011-05-25T22:16:47.668-07:00

A teacher is a compass that activates the magnets of curiosity, knowledge, and wisdom in the pupils.

ERKOhttp://www.blogger.com/profile/01453699893902804035noreply@blogger.com0tag:blogger.com,1999:blog-1859406497159048060.post-74972972937179202542011-05-25T21:57:00.000-07:002011-05-25T21:57:12.556-07:00

I did a little research about TERC (I used to teach from the older version, but it is rather similar as the new one). I would offer this as a suggestion for changing up the scope and sequence: 1. Shape of Data2. Factors, Multiple and Arrays3. Landmark Numbers4. Fraction Cards and Decimal squares (supplement with fractions circles and more mixed number stuff, but I like the connections between

ERKOhttp://www.blogger.com/profile/01453699893902804035noreply@blogger.com0tag:blogger.com,1999:blog-1859406497159048060.post-48317900705644055052011-05-25T21:29:00.000-07:002011-05-25T21:30:14.264-07:00

We all should be encouraging respect for teachers.  They know more than students about a great deal of things. They try REALLY hard to share what they know and how they know it. They respect effort. Let's respect their effort as well.

ERKOhttp://www.blogger.com/profile/01453699893902804035noreply@blogger.com0tag:blogger.com,1999:blog-1859406497159048060.post-26635076679462037482011-05-25T21:21:00.000-07:002011-05-25T22:09:47.216-07:00

As the fourth grade math year runs to it end, consider this: Were fractions at least a quarter to a third of the math you covered during the year? Did you know that fractions: equivalence, like denominators and mixed numbers are one of 3 focus standards in the new Common Core Standards adopted by many (almost all) of the 50 states in the US? A clear understanding and broad base of experience with

ERKOhttp://www.blogger.com/profile/01453699893902804035noreply@blogger.com1tag:blogger.com,1999:blog-1859406497159048060.post-82431828168117243382011-05-25T17:10:00.001-07:002011-05-25T17:10:52.900-07:00

Best is good. Better is best.

ERKOhttp://www.blogger.com/profile/01453699893902804035noreply@blogger.com0tag:blogger.com,1999:blog-1859406497159048060.post-44217581131260419422011-05-24T21:17:00.000-07:002011-05-24T21:19:28.001-07:00

A College Degree Pays but Major Important for Making Money - ABC News That English major might seem more fun than math or engineering, but it won't pay off nearly as well in the long run, according to a Georgetown University study released today. Researchers compared the average earnings for various fields over a 40-year career and found a 300 percent difference between the average salary of

ERKOhttp://www.blogger.com/profile/01453699893902804035noreply@blogger.com0tag:blogger.com,1999:blog-1859406497159048060.post-37432887158868141472011-05-24T21:05:00.000-07:002011-05-24T21:05:59.432-07:00

Yep! Our school ends on the Friday before Memorial Day Weekend. We started in the second week of August, so our 176 days of school (4 furlough days discounted) are about to finish up. This has been the best classroom I have ever had the opportunity to occupy. I will miss it, but more importantly, will miss the kids who populated it. I loved teaching ancient history, but starting next year I

ERKOhttp://www.blogger.com/profile/01453699893902804035noreply@blogger.com0tag:blogger.com,1999:blog-1859406497159048060.post-14723081210041599422011-05-24T20:50:00.000-07:002011-05-24T21:39:41.550-07:00

In his foreword to Skemp’s The Psychology of Learning Mathematics, Foss stated that mathematics is a curious subject, psychologically. It seems to divide people into two camps…there are those who can do mathematics and there are those who cannot, or who think they cannot, and who "block" at the first drop of a symbol. (cited in Skemp, 1971, p.9) Math Anxiety is a topic that interests me. I am

ERKOhttp://www.blogger.com/profile/01453699893902804035noreply@blogger.com0tag:blogger.com,1999:blog-1859406497159048060.post-84069182625072426752011-05-24T16:18:00.000-07:002011-05-24T16:18:45.031-07:00

I am a newbie to Linkedin. In fact, I didn't want to join yet another social network (same connections, new passwords = ugh!) But it seems that it might be a good idea to join, set up a professional network as I look to spread out my wings a little and try towards new horizons. So I looked around and saw this info graphic ( I like to work these things out via NUMBERS ). From: http://

ERKOhttp://www.blogger.com/profile/01453699893902804035noreply@blogger.com0tag:blogger.com,1999:blog-1859406497159048060.post-16005184544252744392011-05-24T07:56:00.000-07:002011-05-24T07:56:56.808-07:00

I found this article very illuminating. It takes mathematics and applies it directly to a political issue. Rather than fanning the flames of partisanship, it cooly looks at the issue of taxes from a more pragmatic point of view. That is another thing I love about math! My wife and I run a small lodging business in a resort town in New Mexico, employing eight people. Income from that

ERKOhttp://www.blogger.com/profile/01453699893902804035noreply@blogger.com0tag:blogger.com,1999:blog-1859406497159048060.post-58650556000039693452011-05-24T07:50:00.000-07:002011-05-24T07:50:10.338-07:00

No tree has branches so foolish as to fight amongst themselves.  — Ojibwa Indian Saying

ERKOhttp://www.blogger.com/profile/01453699893902804035noreply@blogger.com0tag:blogger.com,1999:blog-1859406497159048060.post-61787726028207348442011-05-23T22:03:00.000-07:002011-05-24T07:50:36.570-07:00

Thinking that good teachers are like good basketball players - Don't panic, make adjustments on the the run, and never give up.

ERKOhttp://www.blogger.com/profile/01453699893902804035noreply@blogger.com0tag:blogger.com,1999:blog-1859406497159048060.post-52778126808023151942011-05-23T21:23:00.000-07:002011-05-25T22:11:34.539-07:00

I am a big fan of the Common Core Standards. I think they bring rationality and clarity to a complex field. I love how they build upon themselves logically both within a grade level and amongst them. Here is what the Common Core standards say in their 4th grade introduction: In Grade 4, instructional time should focus on three critical areas: (1) developing understanding and fluency with

ERKOhttp://www.blogger.com/profile/01453699893902804035noreply@blogger.com0tag:blogger.com,1999:blog-1859406497159048060.post-3266232998006132892011-05-23T13:26:00.000-07:002011-05-23T13:26:14.714-07:00

Singapore Strengths Framework: The study indicates there is a correlation between focused frameworks such as those used in Singapore and good test performance. Singapore offers an alternative mathematics framework for lower-performing students that covers all the mathematics topics in the regular framework, but at a slower pace and with greater repetition, and with support from expert teachers.

ERKOhttp://www.blogger.com/profile/01453699893902804035noreply@blogger.com0tag:blogger.com,1999:blog-1859406497159048060.post-11140190761694031702011-05-23T09:14:00.001-07:002011-05-23T09:14:44.571-07:00

"Why is it that nobody understands me, yet everybody likes me?"  Albert Einstein

ERKOhttp://www.blogger.com/profile/01453699893902804035noreply@blogger.com0tag:blogger.com,1999:blog-1859406497159048060.post-27701595616426904862011-05-23T07:52:00.000-07:002011-05-23T07:54:45.134-07:00

Game of Thrones is a great show, thanks to its heavy reliance on character development, political intrigue, and suspense – not to mention the excellent acting from all parties involved. I will say that it beats the book for me, which is not something I say lightly. The story moves more fluidly and the characters are easier to distinguish in the show when compared to the book. I watch it on my

ERKOhttp://www.blogger.com/profile/01453699893902804035noreply@blogger.com0tag:blogger.com,1999:blog-1859406497159048060.post-85144889709500942012011-05-21T18:44:00.000-07:002011-05-21T18:44:37.214-07:00

Question:  If you have a cylinder with a raduis "z" and a height of "a", then what is the volume?  Answer: pizza found on: http://www.mathfail.com/2010/01/pizza-math.html

ERKOhttp://www.blogger.com/profile/01453699893902804035noreply@blogger.com0tag:blogger.com,1999:blog-1859406497159048060.post-75314691288943221642011-05-21T18:37:00.001-07:002011-05-21T18:37:45.563-07:00

In the end, it's not the years in your life that count. It's the life in your years.  ~ Abraham Lincoln

ERKOhttp://www.blogger.com/profile/01453699893902804035noreply@blogger.com0tag:blogger.com,1999:blog-1859406497159048060.post-7189724553107352242011-05-21T18:36:00.000-07:002011-05-21T18:36:34.066-07:00

I don't join in the crowds making fun of this "rapture" thing, but here is a small article on the math around it: "Harold Camping, who has gone on record as saying the world was created in 11,013B.C., believes the Bible teaches that the flood of Noah’s day was in 4990 B.C.Camping, leader of the Oakland-based ministry Family Radio Worldwide, then points to the Apostle Peter in the 1st century

ERKOhttp://www.blogger.com/profile/01453699893902804035noreply@blogger.com0tag:blogger.com,1999:blog-1859406497159048060.post-89472577729026473342011-05-19T22:11:00.000-07:002011-05-19T22:12:18.861-07:00

Public School Teaching is only profession judged by someone else's work over which they have NO sanction or control.

ERKOhttp://www.blogger.com/profile/01453699893902804035noreply@blogger.com0tag:blogger.com,1999:blog-1859406497159048060.post-61844626239872980782011-05-19T14:36:00.000-07:002011-05-19T14:36:21.319-07:00

Scientists at Queen Mary, University of London and Royal Holloway, University of London have discovered that bees learn to fly the shortest possible route between flowers even if they discover the flowers in a different order. Bees are effectively solving the 'Travelling Salesman Problem', and these are the first animals found to do this.The Travelling Salesman must find the shortest route that

ERKOhttp://www.blogger.com/profile/01453699893902804035noreply@blogger.com0tag:blogger.com,1999:blog-1859406497159048060.post-31639272758864557562011-05-19T12:08:00.001-07:002011-05-19T12:08:55.997-07:00

Take a long rope; tie it to the bottom of the goal post at one end of a football field. Then run it across the length of the field (120 yards) to a goal post at the other end.  Stretch it tightly, and then tie it to the bottom of that goal post, so that it lies flat against the ground. Now suppose that I add just 1 foot of slack to the rope, so that now I can lift it off the ground at the 50-

ERKOhttp://www.blogger.com/profile/01453699893902804035noreply@blogger.com6tag:blogger.com,1999:blog-1859406497159048060.post-26761361944163312492011-05-19T10:14:00.001-07:002011-05-19T10:14:58.828-07:00

Act as if what you do makes a difference. It does.  William James

ERKOhttp://www.blogger.com/profile/01453699893902804035noreply@blogger.com0tag:blogger.com,1999:blog-1859406497159048060.post-3271436484095784592011-05-18T22:01:00.000-07:002011-05-18T22:02:23.764-07:00

Carolyn Felux answered the following question about working with a math coach.Q. My district has begun using a math coach model, and now I have a full-time math coach in my building. What should I expect the math coach to do, and how should I work with, and support, her?A. Having a math coach at your school is an excellent way to support teachers and explore best practices for improved math

ERKOhttp://www.blogger.com/profile/01453699893902804035noreply@blogger.com0tag:blogger.com,1999:blog-1859406497159048060.post-13054595887902501462011-05-18T21:44:00.000-07:002011-05-18T21:44:10.306-07:00

I was gratified to be able to answer promptly, and I did. I said I didn't know.  Mark Twain

ERKOhttp://www.blogger.com/profile/01453699893902804035noreply@blogger.com0tag:blogger.com,1999:blog-1859406497159048060.post-82921524194449900992011-05-18T21:35:00.000-07:002011-05-18T21:35:26.102-07:00

California Gov. Jerry Brown has taken a big step towards reducing the testing mania in the nation's most populous state. Gov. Jerry Brown is proposing to suspend funding for CALPADS, the state student longitudinal data system, and to stop further planning for CALTIDES, the teacher data base that was to be joined at the hip with CALPADS.‘A number of problems have been identified with California’s

ERKOhttp://www.blogger.com/profile/01453699893902804035noreply@blogger.com1tag:blogger.com,1999:blog-1859406497159048060.post-30314099071906731542011-05-18T21:27:00.001-07:002011-05-18T21:27:40.232-07:00

ERKOhttp://www.blogger.com/profile/01453699893902804035noreply@blogger.com1tag:blogger.com,1999:blog-1859406497159048060.post-79298002504799650512011-05-18T08:19:00.000-07:002011-05-18T08:19:53.229-07:00

Vermont per student education budget = $15,500 + California per student education budget = $7,500 Do the math!

ERKOhttp://www.blogger.com/profile/01453699893902804035noreply@blogger.com2tag:blogger.com,1999:blog-1859406497159048060.post-35552277904408818182011-05-18T07:36:00.000-07:002011-05-18T07:36:30.864-07:00

Let us, then be up and doing, With a heart for any fate;Still achieving, still pursuing,Learn to labour and to wait.Henry Wadsworth Longfellow

ERKOhttp://www.blogger.com/profile/01453699893902804035noreply@blogger.com0tag:blogger.com,1999:blog-1859406497159048060.post-86831148509578800642011-05-17T20:46:00.000-07:002011-05-17T20:46:34.213-07:00

Factoring Using the Area Model

ERKOhttp://www.blogger.com/profile/01453699893902804035noreply@blogger.com0tag:blogger.com,1999:blog-1859406497159048060.post-73942734943211724212011-05-17T20:29:00.001-07:002011-05-17T20:30:54.309-07:00

Teachers: Don't find fault, find a remedy. Henry Ford

ERKOhttp://www.blogger.com/profile/01453699893902804035noreply@blogger.com0tag:blogger.com,1999:blog-1859406497159048060.post-9608180607070423712011-05-17T20:13:00.001-07:002011-05-18T09:09:37.769-07:00

Extraversion (E) versus Introversion (I)Extraverts find energy in things and people.Introverted students want to develop frameworks that integrate or connect the subject matter.Sensing (S) versus Intuition (N)Sensing people are detail oriented, want facts, and trust them.Intuitive people seek out patterns and relationships among the facts they have gathered. Thinking (T) versus Feeling (F)

ERKOhttp://www.blogger.com/profile/01453699893902804035noreply@blogger.com1tag:blogger.com,1999:blog-1859406497159048060.post-32696136756887083742011-05-17T16:16:00.000-07:002011-05-17T16:17:59.119-07:00

THIS IS WHAT I WILL BE DOING NEXT YEAR: PRIME is a California Math/Science Partnership between three organizations:San Francisco Unified School District (SFUSD) San Francisco State University (SFSU) Bay Area Math Project at the Lawrence Hall of Science GoalsThe partnership aims to deepen math content knowledge for 4th and 5th grade teachers in SFUSD through a three year sequence of 5-day summer

ERKOhttp://www.blogger.com/profile/01453699893902804035noreply@blogger.com1tag:blogger.com,1999:blog-1859406497159048060.post-10075407783227508522011-05-17T07:55:00.000-07:002011-05-17T16:20:21.430-07:00

At Big Fat Math you can learn how much activity it will take to burn-off fast food, soft drink and junk food products. http://www.bigfatmath.com/index.aspx

ERKOhttp://www.blogger.com/profile/01453699893902804035noreply@blogger.com0tag:blogger.com,1999:blog-1859406497159048060.post-21153124066439881622011-05-17T07:48:00.001-07:002011-05-17T07:48:45.968-07:00

To isolate mathematics from the practical demands of the sciences is to invite the sterility of a cow shut away from the bulls. Chebyshev

ERKOhttp://www.blogger.com/profile/01453699893902804035noreply@blogger.com0tag:blogger.com,1999:blog-1859406497159048060.post-39188718910879830362011-05-17T07:43:00.000-07:002011-05-17T07:44:22.445-07:00

Mathematics is not a careful march down a well-cleared highway, but a journey into a strange wilderness, where the explorers often get lost.  - W.S. Anglin In 1974 I was a 12 year old “know-it-all” in Mr. Bott’s 7th grade math class at Oakside Junior High. I was in tough competition with Jack Taniguchi for the coveted first place seat up front and to the left of the blackboard. It was like some

ERKOhttp://www.blogger.com/profile/01453699893902804035noreply@blogger.com2tag:blogger.com,1999:blog-1859406497159048060.post-88034677501819536392011-05-16T22:23:00.001-07:002011-05-16T22:23:54.087-07:00

I received the phone call I wanted today. Starting next August I will be one of two SFUSD math coaches. I am looking forward to this new challenge of working with 20 some odd teachers to improve math instruction.

ERKOhttp://www.blogger.com/profile/01453699893902804035noreply@blogger.com0tag:blogger.com,1999:blog-1859406497159048060.post-72705432391120325372011-05-16T15:52:00.000-07:002011-05-16T15:52:08.307-07:00

Tests are one measure, NOT the purpose, of education.

ERKOhttp://www.blogger.com/profile/01453699893902804035noreply@blogger.com1tag:blogger.com,1999:blog-1859406497159048060.post-10133942519603621242011-05-15T17:32:00.001-07:002011-05-15T17:32:34.340-07:00

ERKOhttp://www.blogger.com/profile/01453699893902804035noreply@blogger.com0tag:blogger.com,1999:blog-1859406497159048060.post-5230268104139113132011-05-15T17:16:00.001-07:002011-05-15T17:16:39.647-07:00

ERKOhttp://www.blogger.com/profile/01453699893902804035noreply@blogger.com0tag:blogger.com,1999:blog-1859406497159048060.post-78836816406144716582011-05-15T17:08:00.000-07:002011-05-15T17:08:14.269-07:00

The person ignorant of mathematics will be increasingly limited in his grasp of the main forces of civilization.   John Kemeny

ERKOhttp://www.blogger.com/profile/01453699893902804035noreply@blogger.com0tag:blogger.com,1999:blog-1859406497159048060.post-73316235646812262832011-05-15T17:02:00.000-07:002011-05-15T17:02:31.270-07:00

Choose a job you love, and you will never have to work a day in your life.  ~ Confucius

ERKOhttp://www.blogger.com/profile/01453699893902804035noreply@blogger.com0tag:blogger.com,1999:blog-1859406497159048060.post-57269797545167043082011-05-15T16:57:00.000-07:002011-05-15T16:57:56.707-07:00

Via @republicmath 

ERKOhttp://www.blogger.com/profile/01453699893902804035noreply@blogger.com0tag:blogger.com,1999:blog-1859406497159048060.post-20778888934205776612011-05-13T12:53:00.000-07:002011-05-13T12:54:06.482-07:00

(actual lockers at my school) Here is a long time favorite middle school math problem: Imagine you are at a school that has 100 lockers, all shut. Suppose the first student goes along the row and opens every locker. The second student then goes along and shuts every other locker beginning with locker number 2. The third student changes the state of every third locker

ERKOhttp://www.blogger.com/profile/01453699893902804035noreply@blogger.com0tag:blogger.com,1999:blog-1859406497159048060.post-40477677848146356042011-05-13T12:04:00.000-07:002011-05-13T12:06:22.702-07:00

Just before my job changed last year, I had embarked on a modernization of some the technology I used in my 8th grade algebra class. In particular, I sold off all the TI-83 graphing calculators and used the money (plus a little more) to buy a class set of iPod Touches. I had a plan to install several very useful tools on these iPods, but my favorite one was the Graphing Calculator App: http://

ERKOhttp://www.blogger.com/profile/01453699893902804035noreply@blogger.com0tag:blogger.com,1999:blog-1859406497159048060.post-18519090184298156432011-05-13T11:59:00.001-07:002011-05-13T11:59:20.014-07:00

When the mind is thinking it is talking to itself.   Plato

ERKOhttp://www.blogger.com/profile/01453699893902804035noreply@blogger.com0tag:blogger.com,1999:blog-1859406497159048060.post-10793447732328847022011-05-13T11:53:00.001-07:002011-05-13T11:53:59.118-07:00

ERKOhttp://www.blogger.com/profile/01453699893902804035noreply@blogger.com0tag:blogger.com,1999:blog-1859406497159048060.post-8098298488743654362011-05-11T18:03:00.000-07:002011-05-13T13:37:02.227-07:00

Still abstract, but a way to "hang" a concept on a manipulative. With careful use, these can be very powerful.

ERKOhttp://www.blogger.com/profile/01453699893902804035noreply@blogger.com0tag:blogger.com,1999:blog-1859406497159048060.post-18896377885674900732011-05-11T08:36:00.000-07:002011-05-11T08:36:21.122-07:00

I have not been a huge fan of Houghton Mifflin math programs in the past, but I am also against these huge, heavy and overly busy algebra books that come to be the first and most lasting impression our students have of what should be a beautiful algebra experience. That being said, the very idea of have a dynamic algebra app for the iPad or some other tablet seems to me to be a winner. The

ERKOhttp://www.blogger.com/profile/01453699893902804035noreply@blogger.com0tag:blogger.com,1999:blog-1859406497159048060.post-68448241731362304832011-05-11T08:07:00.000-07:002011-05-11T08:07:17.002-07:00

Be not the first by whom the new are tried, Nor yet the last to lay the old aside. - Alexander Pope

ERKOhttp://www.blogger.com/profile/01453699893902804035noreply@blogger.com0tag:blogger.com,1999:blog-1859406497159048060.post-1459903724851113612011-05-10T15:42:00.000-07:002011-05-10T15:42:26.989-07:00

According to some, algebraic thinking is:  Kaput (NCTM, 1993): Algebraic thinking involves the construction and representation of patterns and regularities, deliberate generalization, and most important, active exploration and conjecture. Greenes and Findell (1998): The big ideas of algebraic thinking involves representation, proportional reasoning, balance, meaning of variable, patterns and

ERKOhttp://www.blogger.com/profile/01453699893902804035noreply@blogger.com0tag:blogger.com,1999:blog-1859406497159048060.post-40738768745132686212011-05-10T15:26:00.000-07:002011-05-10T15:27:16.187-07:00

I am not a big fan of text messages, but recently I have come to see the ease with which basic messages can get transmitted without a lot of confusion or run-around. Most of my students, even the poorer ones, have cell phones and are apt texters. Nearly all of the parents have abandoned land line phones in favor of cell phones. I am thinking that instead of resisting texting, I should embrace it

ERKOhttp://www.blogger.com/profile/01453699893902804035noreply@blogger.com0tag:blogger.com,1999:blog-1859406497159048060.post-58386149569436459122011-05-10T10:07:00.001-07:002011-05-10T10:07:18.252-07:00

Don't tell people how to do things, tell them what to do and let them surprise you with their results.  ~ George S. Patton

ERKOhttp://www.blogger.com/profile/01453699893902804035noreply@blogger.com0tag:blogger.com,1999:blog-1859406497159048060.post-70320173578377122302011-05-10T10:04:00.000-07:002011-05-10T10:04:44.222-07:00

Time to take Pythagorean Theorem and the idea of square roots to a new level. I love the patterns discovered so clearly while working on Theodorus' Wheel in class. After they make the wheel, I ask them to imagine them as part of an art project. They make hats, baby carriages, snail shells, Princess Lea's hairdo etc. Here is what Theodorus' Wheel is: The Wheel Of Theodorus, or Square Root Spiral,

ERKOhttp://www.blogger.com/profile/01453699893902804035noreply@blogger.com0tag:blogger.com,1999:blog-1859406497159048060.post-13169501138530029282011-05-09T10:01:00.001-07:002011-05-09T10:01:33.398-07:00

More teachers rely on coercion and extrinsic inducements, the less likely students are going to be interested in what they are induced to do.

ERKOhttp://www.blogger.com/profile/01453699893902804035noreply@blogger.com0tag:blogger.com,1999:blog-1859406497159048060.post-30411382733037739182011-05-09T09:19:00.001-07:002011-05-10T10:08:35.087-07:00

  A parent recently wrote requesting advise on how to help her student  round her answers for a POW problem. It reminded me of how many times I write comments to students asking them to reconsider the reasonableness of their answers. In fact, many problems based on the real world are answered more effectively with rounded numbers, yet I continually see numerical answers carried deeply into

ERKOhttp://www.blogger.com/profile/01453699893902804035noreply@blogger.com2tag:blogger.com,1999:blog-1859406497159048060.post-37269094701559293302011-05-06T19:06:00.000-07:002011-05-09T10:09:30.318-07:00

High and middle schools of the US do not encourage enough critical thinking among our students.  Everything is being done with guidance of a teacher going through steps of a procedure - and this is where the problem is.  For example, in Math: Teachers provide step-by-step instructions how to solve an equation, how to divide, how to... This does not teach students how to think about math

ERKOhttp://www.blogger.com/profile/01453699893902804035noreply@blogger.com0tag:blogger.com,1999:blog-1859406497159048060.post-45378761287820674522011-05-06T19:03:00.000-07:002011-05-06T19:03:26.148-07:00

Arthur Benjamin's formula for changing math education | Video on TED.com

ERKOhttp://www.blogger.com/profile/01453699893902804035noreply@blogger.com0tag:blogger.com,1999:blog-1859406497159048060.post-85862534339345042062011-05-06T17:57:00.001-07:002011-05-09T10:02:16.336-07:00

It doesn't matter who you are, or where you came from. The ability to triumph begins with you. Always. Oprah Winfrey

ERKOhttp://www.blogger.com/profile/01453699893902804035noreply@blogger.com0tag:blogger.com,1999:blog-1859406497159048060.post-6451734954718578722011-05-06T17:53:00.001-07:002011-05-06T17:53:27.377-07:00

What Algebra should we teach?Algebra is fundamental to understanding mathematical thought. It encompasses an understanding of patterns and functions, ways of representing and analyzing mathematical structures and situations, models that represent quantitative ideas and relationships, and approaches that analyze change in a variety of situations. Most people recognize that algebra is needed by

ERKOhttp://www.blogger.com/profile/01453699893902804035noreply@blogger.com0tag:blogger.com,1999:blog-1859406497159048060.post-56605561862425685862011-04-27T23:40:00.000-07:002011-04-27T23:40:17.072-07:00

Wow! Reading through this blog reminds be yet again how quickly time flies by. Almost one year has gone by since I last took care of this blog. My job changed. I left math and went back to Spanish Immersion: 6th grade : Ancient History. I love what I'm doing, but miss math. Miss it a lot. Enough to return, hopefully. So I dusted the bytes off this blog and will revive it. I'm excited!

ERKOhttp://www.blogger.com/profile/01453699893902804035noreply@blogger.com1tag:blogger.com,1999:blog-1859406497159048060.post-32069088701637282472010-07-06T14:08:00.000-07:002011-05-09T10:03:05.046-07:00

Las imposibilidades probable se prefieren a las posibilidades inprobables. Probable impossibilities are to be preferred to improbable possibilities. Aristotle

ERKOhttp://www.blogger.com/profile/01453699893902804035noreply@blogger.com0tag:blogger.com,1999:blog-1859406497159048060.post-31398800466748992602010-05-23T20:29:00.001-07:002010-05-23T20:29:23.517-07:00

An effective leader is: 1.  Able: demonstrates competence, expertise, experience, and capability in getting the desired results accomplished 2.  Believable: walks the talk of a core set of values, demonstrates honesty, and uses fair, equitable practices 3.  Connected: interacts with staff, communicates and shares relevant information, provides praise, and gives recognition 4.  Dependable: is

ERKOhttp://www.blogger.com/profile/01453699893902804035noreply@blogger.com0tag:blogger.com,1999:blog-1859406497159048060.post-60857000212197138092010-05-20T08:53:00.001-07:002010-05-21T13:00:46.364-07:00

The title of this POW is Going Global. In this problem you have to figure out the area of the field of Shakespeare’s Globe Theater. Using this you have to figure out how many people can stand in the field if they each need 4 square feet. The theater is an icosagon, this is a 20 sided figure. You have to figure out the interior angle. To figure out these problems you have to assume that the inner

ERKOhttp://www.blogger.com/profile/01453699893902804035noreply@blogger.com0tag:blogger.com,1999:blog-1859406497159048060.post-31683877267766826032010-05-11T13:39:00.000-07:002010-05-19T08:01:07.125-07:00

Hilarious, to love a boy who’s hilarious awesome and crucial to be full of awe so full of well-spring so dripping with hope, really for a boy who’s nine. So be it, then: hilarious.

ERKOhttp://www.blogger.com/profile/01453699893902804035noreply@blogger.com0tag:blogger.com,1999:blog-1859406497159048060.post-1642685520677704662010-05-09T00:52:00.001-07:002011-05-09T10:04:24.555-07:00

An error doesn't become a mistake until you refuse to correct  it. Orlando A. Battista. 

ERKOhttp://www.blogger.com/profile/01453699893902804035noreply@blogger.com0tag:blogger.com,1999:blog-1859406497159048060.post-89260431369613161272010-05-09T00:34:00.000-07:002011-05-09T10:12:19.696-07:00

The end of the school year approaches. It is always bitter sweet for me.

ERKOhttp://www.blogger.com/profile/01453699893902804035noreply@blogger.com0tag:blogger.com,1999:blog-1859406497159048060.post-45912623921623395092010-05-08T11:46:00.003-07:002010-05-08T11:46:12.032-07:00

Life isn’t fair, but it’s still good. Nobody has every said that life is fair, but it seems that in teaching, many people lose their way lamenting this fact. We are the lucky ones. We work in meaningful ways. We get automatic and lovely feedback on our efforts. We sing songs, paint pictures and enjoy a good fable now and then. True: we may have too many papers to grade, too many students to

ERKOhttp://www.blogger.com/profile/01453699893902804035noreply@blogger.com0tag:blogger.com,1999:blog-1859406497159048060.post-13416547061412138652010-05-05T23:23:00.001-07:002010-05-05T23:23:34.857-07:00

Problems of the WeekView more presentations from pepepacha.

ERKOhttp://www.blogger.com/profile/01453699893902804035noreply@blogger.com0tag:blogger.com,1999:blog-1859406497159048060.post-32313875845936983372010-03-28T19:28:00.000-07:002011-05-09T09:53:25.069-07:00

Despite the protests of parents alarmed by the impending formation of a Gay-Straight Alliance club at a Mead Valley middle school, administrators said the Val Verde Unified School District won't stand in the way."We have an open forum policy," said Mike Bazan, spokesman for the district, which serves portions of Perris, Moreno Valley and unincorporated Riverside County. "Any and all student-run

ERKOhttp://www.blogger.com/profile/01453699893902804035noreply@blogger.com1tag:blogger.com,1999:blog-1859406497159048060.post-70195071002450153442010-03-26T21:30:00.000-07:002010-03-26T21:30:30.843-07:00

This is what I believe: Parent-teacher conferences can be a challenging time for all involved.  The parents may or may not feel comfortable in the classroom due to a bad experience as a child or lack of communication from previous teachers.  The student is worried about getting a bad report.  The teacher is concerned about confrontation.  But, if all parties involved are well-informed and are

ERKOhttp://www.blogger.com/profile/01453699893902804035noreply@blogger.com0tag:blogger.com,1999:blog-1859406497159048060.post-11217330876583524432010-03-20T10:56:00.000-07:002010-03-20T10:56:07.460-07:00

The title of this week’s POW was “Captain Future.” In this problem, Captain Future, Joan Rundall, Otho and Grag have to get over a bridge in 17 minutes. There has to be 3 trips going across the bridge and 2 trips coming back over the bridge because a metal box must guide 2 or less people across the bridge at a time. Captain Future can cross the bridge in 1 minute, Joan Rundall can cross the

ERKOhttp://www.blogger.com/profile/01453699893902804035noreply@blogger.com0tag:blogger.com,1999:blog-1859406497159048060.post-55668653128049784452010-03-19T09:17:00.001-07:002010-03-19T09:17:36.325-07:00

The title of this week's P.O.W is Unraveling. In this problem, the Captain finds a book called Our Historyand in it, she reads about Captain of the Ferdinando, Jurakan, who made seven journeys around the Carribean. On each of those seven journeys, he got a famous treasure which he deafeted an opponent to get. In this problem, you have to find out the order of his voyage and each of the people he

ERKOhttp://www.blogger.com/profile/01453699893902804035noreply@blogger.com0tag:blogger.com,1999:blog-1859406497159048060.post-34299661988782061822010-03-17T11:09:00.000-07:002010-03-17T11:09:29.283-07:00

A hearing has been scheduled in the case of Constance McMillen, the Mississippi lesbian high school student whose story has made national headlines after her school canceled the prom because she wanted to bring a female date. The ACLU is suing the Itawamba School District. The AP reports: "In the court documents, McMillen said Rick Mitchell, the assistant principal at the school, told her she

ERKOhttp://www.blogger.com/profile/01453699893902804035noreply@blogger.com1tag:blogger.com,1999:blog-1859406497159048060.post-23657009334324058552010-03-14T18:04:00.001-07:002010-03-14T18:04:46.641-07:00

ERKOhttp://www.blogger.com/profile/01453699893902804035noreply@blogger.com0tag:blogger.com,1999:blog-1859406497159048060.post-64012217947674099502010-03-13T21:10:00.000-08:002010-03-13T21:10:46.617-08:00

The San Francisco Unified School District is facing over $113 million in a massive budget shortfall. With state revenues plummeting and no signs of improvement, the district sent out over 900 pink slips last week; 318 of those were sent to schoolteachers.  With the possibility of layoffs increasingly present, Superintendent Carlos Garcia announced a plan to minimize expenditures. Some of his

ERKOhttp://www.blogger.com/profile/01453699893902804035noreply@blogger.com0tag:blogger.com,1999:blog-1859406497159048060.post-24677173246679129902010-03-09T09:43:00.000-08:002010-03-09T09:43:46.461-08:00

ERKOhttp://www.blogger.com/profile/01453699893902804035noreply@blogger.com0tag:blogger.com,1999:blog-1859406497159048060.post-36519600831654944552010-03-03T11:06:00.000-08:002010-03-03T11:06:14.178-08:00

Supportive leadership is more likely to keep effective teachers in the classroom than higher pay, according to a teacher survey sponsored by the Bill & Melinda Gates Foundation along with Scholastic. Teachers also said they valued "relevant" professional development, safe working conditions and having time to collaborate with other educators. Of the teachers who were surveyed, 59% said that

ERKOhttp://www.blogger.com/profile/01453699893902804035noreply@blogger.com0tag:blogger.com,1999:blog-1859406497159048060.post-47376095453406981322010-03-02T21:51:00.001-08:002011-05-09T10:06:16.366-07:00

To exist is to change, to change is to mature, to mature is to go on creating oneself endlessly. Henri Bergson

ERKOhttp://www.blogger.com/profile/01453699893902804035noreply@blogger.com0tag:blogger.com,1999:blog-1859406497159048060.post-73565626111746644002010-03-02T08:08:00.000-08:002010-03-02T08:08:05.637-08:00

From the The March/April 2009 issue of the Stanford Magazine GOLDEN RULES The article on Tom Wyman and his slide rule collection (“Calculating Collector,” Red All Over, January/February) takes me back to 1972, when Hewlett Packard introduced the HP-35, its first pocket scientific calculator, priced at $395. I was living in Palo Alto then, so I went to the Stanford Bookstore to see it. I

ERKOhttp://www.blogger.com/profile/01453699893902804035noreply@blogger.com0tag:blogger.com,1999:blog-1859406497159048060.post-31935399260731820042010-03-01T16:24:00.000-08:002010-03-01T16:27:16.436-08:00

          Mr. Bott was surprised to see Mr. LeFour at his classroom door. He couldn’t remember the last time they had spoken to each other in the past couple of years. Ever since Mr. LeFour was hired and took over the sport department from Mr. Bott, there had been friction. Mr. Bott had dedicated many years to Willowside Middle School’s sports teams. True, the school rarely had a winning season,

ERKOhttp://www.blogger.com/profile/01453699893902804035noreply@blogger.com0tag:blogger.com,1999:blog-1859406497159048060.post-11181921534025121282010-02-28T22:31:00.000-08:002010-02-28T22:31:53.074-08:00

One lesson I learned well as a kindergarten teacher: allow lots of free exploration of materials before attempting to teach with them. As a middle school teacher, I think this is even more imperative. As an introduction to polyhedrons, I asked my students to play with wooden polyhedrons at their tables without any rules other than playing safe and fairly. Out of an 80 minutes session, I gave

ERKOhttp://www.blogger.com/profile/01453699893902804035noreply@blogger.com1tag:blogger.com,1999:blog-1859406497159048060.post-41687434163432790952010-02-27T12:01:00.000-08:002010-02-27T12:01:21.642-08:00

I've learned that it's taking me a long time to become the teacher I wanted to be.I've learned that I can keep going long after I can't.I've learned that we are responsible for what we do, no matter how we feel.I've learned that either I control my attitude or it controls me.I've learned that heroes are the people who do what has to be done when it needs to be done, regardless of the consequences

ERKOhttp://www.blogger.com/profile/01453699893902804035noreply@blogger.com0tag:blogger.com,1999:blog-1859406497159048060.post-40261863103585669762010-02-26T11:18:00.000-08:002010-02-26T11:18:10.120-08:00

Ideally the assessment process informs the teacher and the learner about learner progress and at the same time, contributes to the learning process. In theory, good assessment:measures meaningful learning outcomes does so in a fair, reliable, accurate way is easy to administer, score, and interpret informs the teacher about student performance and how they are interpreting course experiences

ERKOhttp://www.blogger.com/profile/01453699893902804035noreply@blogger.com0tag:blogger.com,1999:blog-1859406497159048060.post-55862064603566357602010-02-26T09:42:00.001-08:002010-02-26T09:42:31.717-08:00

Types of Assessment• Pre-Testing You might find it helpful to find out whether your students meet the basic knowledge and skill levels required to learn your materials. Use a pre-test to find out. Pre-tests are often paired with remedial materials. Some teachers offer self-assessment pre-tests prior to the beginning day of class and offer students ways to catch up before the first day. Others

ERKOhttp://www.blogger.com/profile/01453699893902804035noreply@blogger.com2tag:blogger.com,1999:blog-1859406497159048060.post-76563761029656014882010-02-26T09:25:00.000-08:002010-02-26T09:25:36.190-08:00

What is the most important part of teaching?  Many people may say that it is the teaching. But in reality, isn't it the learning? Along those line, I feel that assessing what has been learned is most crucial. But assessing student understanding is the most complex part of the teaching cycle. Teachers must be fair and respectful when assessing students. I believe all students need to be

ERKOhttp://www.blogger.com/profile/01453699893902804035noreply@blogger.com3tag:blogger.com,1999:blog-1859406497159048060.post-20524931155347982782010-02-24T09:16:00.001-08:002010-02-24T09:16:10.223-08:00

Occurring somewhere between the surety of the known and the uncertainty of the unknown, the act of listening is similar to the project of education. It is, after all, when we are not certain that we are compelled to listen. Our listening is always and already in the transformative space of learning. Brent Davis from Teaching Mathematics

ERKOhttp://www.blogger.com/profile/01453699893902804035noreply@blogger.com0tag:blogger.com,1999:blog-1859406497159048060.post-58778282125705082962010-02-21T22:45:00.000-08:002010-02-21T22:45:42.783-08:00

Cynthia lay in her hammock, exhausted yet unable to rest. Nothing on this trip seemed real now. Not even 24 hours earlier she was on the Rim with the Adults. There had been hope of finding a way off this confusing island. Then the rocks came hurling through the sky. She saw Jesse hit in the head and fall, then, in short order, Margie and Jeanie and several Adults around them were hit. Then

ERKOhttp://www.blogger.com/profile/01453699893902804035noreply@blogger.com0tag:blogger.com,1999:blog-1859406497159048060.post-6780148778647423262010-02-21T16:37:00.000-08:002010-02-21T16:37:08.455-08:00

The teacher drives students; the leader coaches them.  The teacher depends upon authority; the leader on good will.  The teacher inspires fear; the leader inspires enthusiasm.  The teacher says ‘I’; the leader says ‘we.’  The teacher assigns the task, the leader sets the pace.   The teacher fixes the blame for the learning breakdown; the leader fixes the breakdown.  The teacher knows how it

ERKOhttp://www.blogger.com/profile/01453699893902804035noreply@blogger.com1tag:blogger.com,1999:blog-1859406497159048060.post-62931906236029860012010-02-21T13:43:00.000-08:002010-02-21T13:43:15.532-08:00

One of my favorite topics in math is actually HISTORY. All too often we treat MATHEMATICS like some monolithic and pure subject, devoid of the quirks of human nature. But as Spock (Star Trek) so clearly stated, "We are essentially irrational beings." And mathematics is a part of it all. Each year I have my 7th graders do a mini research project I call "On the Shoulders of Giants" (a quote

ERKOhttp://www.blogger.com/profile/01453699893902804035noreply@blogger.com0tag:blogger.com,1999:blog-1859406497159048060.post-73170462642677094642010-02-20T21:47:00.001-08:002010-02-20T21:47:11.475-08:00

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