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Whole Number Division with Semi-Concrete Base Ten Blocks

§ August 26th, 2011 § 4 Comments- Add yours§ Filed under Teaching Math, Technology in Education § Tagged , , , , , , , , , , ,

Helping children develop conceptual understandings, making math learning relevant, and integrating discovery and skills-based learning are all important.

In the blog post The First Steps in Developing Conceptual Understanding of Place Value I shared my 2nd grade grandson’s experience in learning two and three digit addition and subtraction.  He had been learning to add and subtract digits without any understanding of place value, so I introduced the operations using non-proportional objects to teach re-grouping. § Read the rest of this entry…


Relevance: Discovery, Skills-based, and Manipulatives

§ August 23rd, 2011 § 4 Comments- Add yours§ Filed under Teaching Math § Tagged , , , , , , , , , , , , ,

Recently I penned My Last Math Class and shared how I made math learning real for an unique group of students.  Following on its heels, I shared information on the 3 R’s —Rigor, Relevance, and Relationships— coined in 2010 by The International Center for Leadership in Education.

Now I want to expand this theme into another area of math education and discuss what is more meaningful and effective — discovery learning or skills-based learning.  Much material is available to fuel this debate, but I don’t lean towards one or the other.  I am quite comfortable with my seat on the fence, where I have a vantage point. § Read the rest of this entry…


Rigor, Relevance and Relationships Can Make a Difference

§ August 19th, 2011 § 8 Comments- Add yours§ Filed under Instructional Frameworks § Tagged , , ,

artwork by Steve Heath

After the blog post, My Last Math Class, was re-tweeted many times last week, I realized that making math relevant for our students is important to a lot of people.  If that’s the case, then the Rigor/Relevance Framework should be of interest to our readers. § Read the rest of this entry…


My Last Math Class

§ August 8th, 2011 § 7 Comments- Add yours§ Filed under Teaching Math § Tagged , , , , , , , , , , ,

The last year of teaching middle school math was over 25 years ago. Years away were NCLB, high-stakes testing, RTI Tiers I-III, and teacher accountability. By law, kids were allowed to drop out of school once they reached the age of 16, and kids who had not passed all subjects in the 8th grade were not allowed to advance into high school. As a result the middle school teachers had a pool of kids just biding their time.

In my last year with that district I had classes of 8th graders who were 14 – 16 years old, mostly boys who had no interest in learning much of anything. These were the tough classes.  The classes no one else wanted. The kids who were already 16 willingly shared that they were at school to hang out with friends, eat free breakfast and lunch, and to sleep.  Easy to conclude, these kids had not been and were not successful in math. § Read the rest of this entry…


Scientist? It’s Time to Change the Image!

§ August 1st, 2011 § 3 Comments- Add yours§ Filed under Females and Minorities in STEM § Tagged , , , , , , , , , , , , , , , ,


photography by JD Hancock

Play along with me just for a moment.  Be honest now.  When I say the word “scientist,” what is the first image that comes to mind?  Write down a few words that describe that image.  Are you finished?  When you are, read the following account of what happened at a recent school meeting.

Gearing up for the opening of the 2011-2012 school year, over 200 principals and assistant principals of a city school district recently attended a leadership institute with a particular emphasis on instructional leadership.  One of the sessions during the three-day meeting had participants draw the image that first came to mind when given the same word I gave you —scientist.  Before revealing the results, it is important to note that more than half of the people in the leadership positions were female and half were minorities. § Read the rest of this entry…


Does It Take a ‘Th.D.’ to Understand the Pythagorean Theorem or Just an Internet Search?

§ July 25th, 2011 § 1 Comment- Add yours§ Filed under Teaching Math § Tagged , , , , , , , , , , , , ,

“Back where I come from, we have universities, seats of great learning, where men go to become great thinkers.  And when they come out, they think deep thoughts and with no more brains than you have,” as stated by the Wizard from Oz in 1939.  According to him, a Th.D. diploma (Doctor of Thinkology) is all that is needed for Scarecrow to spout off the Pythagorean theorem (albeit his definition was slightly off).  I think my middle school math students would have supported the Wizard’s notion that it takes some kind of diploma to be able to understand the theorem and recite it, but that was before the days of the Internet.  Nowadays, anyone who has any  kind web-surfing device and web access can find a wealth of information about the theorem.  No diploma required!  Just do a Google, Yahoo or Bing search.

Newly posted on YouTube is an animated illustration and explanation of the theorem.  This is a short sequence from a lesson (M8.7) in the Elevated Math app. Another Elevated Math lesson (A18.4) uses the Pythagorean theorem in finding distance between two points. Elevated Math is in the App Store in iTunes.

In your Internet search you will find teaching videos that feature robotic teachers, boring lectures, great info with no people, waterwheels demonstrating the concept, Darth Vadar explaining the theorem,  and even § Read the rest of this entry…


Teaching Math without Words Can Be Done

§ July 21st, 2011 Comments Off§ Filed under From the Elevated Math Team, Other Voices § Tagged , , , , , , , , ,

It has often been said that math is a language all to itself, that it is the universal language because speakers of all other languages share it.   Okay.  I accept that adage.  Even though I believe it, I still have questions as to how it would play out in an actual classroom, in particular an ESL classroom not only with children who speak different languages but also with differing abilities.

In the accompanying YouTube video Matthew Peterson explains how removing the language barrier when students learn mathematics can actually improve language skills.  Through interactive computer software games that provide informative visual feedback, students are taught how and why math works.  He explains that when kids play an active role in figuring things out, they want to talk about it; sharing what they have learned helps them improve their language skills.  So, removing the language barrier can actually increase communication. § Read the rest of this entry…


Where Does Math Instruction Begin for a 4th Grader? That is a Good Question.

§ July 11th, 2011 Comments Off§ Filed under From the Elevated Math Team § Tagged , , , , , , ,

photography by jimmiehomeschoolmom

A mother sent an email the other day asking which lessons of Elevated Math would be appropriate for her son.  He had finished 4th grade and was going into 5th,  but he had struggled with several of the concepts in 4th grade math.  She thought the lessons would help him strengthen his understanding, but she didn’t know which lessons to select.  “Which lessons are appropriate for 4th grade math?”  Excellent question.

Which lessons are appropriate for 6th grade math?  For 7th grade math, algebra in particular? Well, it all depends.  It depends on where the student is in his learning quest.  We would not expect a student to begin solving quadratic equations if he did not understand how to multiply two-digit by two-digit numbers, would we?  Of course not.  But knowing which lessons are appropriate for which grade level is much more difficult.  The answer lies in the scope and sequence selected for the subject by the school, school district, state or province.  § Read the rest of this entry…


A New Found Freedom: Let’s Celebrate Learning Independence!

§ July 5th, 2011 § 1 Comment- Add yours§ Filed under From the Elevated Math Team § Tagged , , , , , , ,

photography by Andreas Blixt

Since the U.S. is celebrating Independence Day, I think this is an appropriate time to underscore the reasons why the iPad and the Elevated Math app can bring a new kind of freedom or independence when learning at home, away from home or in the classroom.  Taking creative liberties, I have created an acrostic that reveals the strengths of using the Elevated Math iPad app with students typically in  grades 4 – 9.  Happy 4th of July!  Let’s celebrate the freedom iPads and Elevated Math can bring to learning! § Read the rest of this entry…


The First Steps in Developing Conceptual Understanding of Place Value

§ June 27th, 2011 § 2 Comments- Add yours§ Filed under Teaching Math § Tagged , , , ,

Photography by Kathy Cassidy

In an earlier blog I shared my concern about my eight year-old grandson knowing how to calculate the correct answer when adding two-digit numbers without knowing the value of the digits in the addends or sum.  But helping children understand place value is more than telling them which number is in the ones place and which number is in the tens place or even that the 5 in 54 equals 5 tens.    It takes their active involvement to develop conceptual understanding of this key concept.

Think about your own experience, your child’s or grandchild’s experience when learning to count.  I’m pretty sure  those experiences are similar to mine—that it seems intuitive to use one-to-one correspondence with real objects when learning to count.  One, two, three balls.  Four, five, six books.  However, when learning to count to ten and beyond, it seems that imitation and rote memorization are valued.  To illustrate my point, haven’t we all heard a parent claim that their child can count to 20? § Read the rest of this entry…


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