Archive for March, 2011

Engaging Test Prep Activities: Great for Guided Math

Posted on March 31, 2011. Filed under: Assessment, Common Math Errors, During the Guided Math Lesson, Elementary math, Test prep | Tags: , , |


Christine King is doing some great work around developing thinking and reasoning and test prep!  She has an excellent blog (www.testsavvymath.blogspot.com) and some cool stuff up on her website at www.ckingeducation.com under Math Resources.  I would like to highlight a few of Christine’s Test Savvy Strategies!  The first one is Find and Fix My Error.  In this strategy students are looking for errors and then fixing them.  It’s a brilliant strategy and a way to get students critically thinking about the math!  See the podcast and lesson overview below.

Podcast: Find and Fix My Error (podcast)
Lesson Overview: Find and Fix My Error

 P.S. These aren’t just for test prep…I’ve been playing many of them with the k-2 bunch and they love them.  Children get games and they learn well through them!
Happy Mathing,
Dr. Nicki
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More Spring Math Ideas

Posted on March 26, 2011. Filed under: Classroom environment, Elementary math, Math is a Language | Tags: , |


This is a great spring riddle activity

Here is another one.

One more for good luck!

Happy Mathing,

Dr. Nicki

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Spring Themed Word Problems: Solve in Guided Math Groups

Posted on March 25, 2011. Filed under: Assessment, Elementary math, Math is a Language | Tags: , , , |


Sprng has finally arrived! Yeahhhhh! So here are some spring word problems to get you started. Remember to point out the type of problem.  See problem types.  Also, remember to discuss the various strategies for solving the problems.  Talk about this in depth so the students can see and hear other people’s thinking. Have people share their ideas and show their thinking.  Remember that the Common Core says to show it with objects, drawings and equations.  Tell your students to show their thinking with pictures, words and numbers.

Spring Word Problems

Happy Mathing,

Dr. Nicki

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More about Bar Diagramming: Great Strategies to Teach In Guided Math Groups

Posted on March 19, 2011. Filed under: Assessment, Common Math Errors, Elementary math, Graphic Organizers, Guided math, Guided Math Introduction, Math is a Language, Mathematical Proficiency | Tags: , , , , , , |


Here are 5 good resources that teach you how to use bar diagramming to work out word problems. Pull your students in guided math groups and begin to teach them how to diagram out problems.  Give each group problems that are appropriate for their learning level.  They do this in Singapore, which has some of the highest math scores in the world.  Bar diagramming gets students to focus on the relationships in the problem instead of just heading straight for an operation.

Resource 1

Resource 2

Resource 3

Resource 4

Resource 5 (good pdf on division in general and the first part discusses bar diagramming in particular)

Happy Mathing,

Dr. Nicki

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Bar Diagramming to Solve Word Problems: Great Strategy to Teach in Guided Math Groups

Posted on March 18, 2011. Filed under: Common Math Errors, Differentiated Instruction, During the Guided Math Lesson, Graphic Organizers, Guided math, Math is a Language, Mathematical Proficiency | Tags: , , , , , , , |


Randy Charles wrote a must read monograph on word problems.   In this article he talks about the two main ways that teachers teach words problems: 1) key word approach 2) Polya’s problem solving phases.  He reiterates that research says don’t use the keyword approach!  He also makes a good point about Polya’s phases as being a framework, not a step by step guide to solving problems.  He goes on to talk about how bar diagramming is a visual approach that provides many possibilities for students to approach word problems.  He then gives several examples.  READ THE ARTICLE IT COULD CHANGE THE WAY YOU THINK ABOUT WORD PROBLEMS! Let me know what you think!

Happy Mathing,

Dr. Nicki

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Solving Word Problems Part 1: Work it out In Guided Math Groups

Posted on March 16, 2011. Filed under: Common Math Errors, During the Guided Math Lesson, Math is a Language | Tags: , , , , , , |


Word Problems are one of the biggest challenges for students in math. In 1977, Australian educator Anne Newman discussed five steps that students need to work through in order to solve a word problem successfully–

(1) reading the problem / READING

(2) comprehending what was read /COMPREHENSION

(3) transforming the words into a mathematical strategy/TRANSFORMATION

 (4) applying a mathematical procedure/PROCESS SKILLS

(5) writing the answer/ ENCODING

Her research showed that over 50% of errors that children make occur in the first three steps– before they even begin to solve the problem!

WOW!

She suggested a 5 step protocol for word problem solving error analysis.  She would ask the following questions:

1.       Please read the question to me. If you don’t know a word, leave it out.

2.       Tell me what the question is asking you to do.

3.       Tell me how you are going to find the answer.

4.       Show me what to do to get the answer. “Talk aloud” as you do it, so that I can understand how you are thinking.

5.       Now, write down your answer to the question.

The five questions link to the 5 processes (noted alongside them).  Whereever the student has a break down, this is where the teaching point begins.  Now, if asked to rework the problem and the student gets it right and can self correct, Newman labels this as a careless error.  All other errors are teaching points.  Try this out on your students and let me know what happens.

Reference:

Reference 1 (Be sure to watch the video) 

Happy Mathing,

Dr. Nicki

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Word Problem Error Analysis: Do Student Math Interviews!

Posted on March 16, 2011. Filed under: Uncategorized |


We can learn so much from students’ error patterns!  We need to look very closely at what they are doing and what they are not doing. White (2005) states that

” Mistakes can become entrenched, so error analysis is the first step towards doing something relevant which will remove the cause of the mistake.”  And as I was discussing in yesterday’s post, the Newman error analysis/interview protocol can help us figure out what is going on with students with word problems. White (2005) gives a great synopsis of the protocol.  Here is a summary of that synopsis.

 

The Five Newman Questions/Requests

  1. Please read the question to me: (This identifies Reading Errors)(Be sure to tell the student to tell you if they don’t know a word. (Put an R if there are errors here.)A reading error is when the student’s reading prevents them from understanding the problem.  If they cannot read key words or understand key symbols in the problem so much so that it prevents them from understanding the problem then this is classified as a reading error.

 

2. Tell me, what the question is asking you to do. (This identifies Comprehension Errors). (Record a C if the student has problems.) A comprehension error is when the student can read the whole problem but doesn’t understand what to do.  They did not get the big picture of what was going on in the problem and therefore could not proceed with the problem.

  1. Which method do you use to get your answer? (This checks for Transformation Errors.) (Record a T if there are problems here.) A Transformation error is when the student can read the problem, and comprehends what to do but doesn’t know how to do it.  The student doesn’t know what operation/s to use.  They get stuck.  For example, they don’t know if it is a multiplication or a division problem.

 

4. Show me how you get your answer, and “talk aloud” as you do it, so that I can understand how you are thinking. (This checks for Process Errors.) (Put a P if there are errors here.)  A Process error is when the student can read the problem, comprehend it, knows what to do but can’t do it.  It is when they don’t know how to do it.  For example, they know they need to multiply but they don’t know how.

5. Now, write down your actual answer. (This checks for Encoding Errors –defined as an inability to express the answer in an acceptable form.) (Ask the student to tell you the answer and to explain the answer.)(Record an E if there are errors here.) An Encoding Error is when the student found the answer but can’t write it out as the actual solution to the problem.  They don’t know how to express it as the answer.

Remember that if the student self corrects it could be classified as a CARELESS ERROR and coded with an X. Newman (1977,1983) also said that students make errors due to lack of motivation. Researchers have also found that 70% of word problem errors were at the Comprehension and Transformation levels  (Marinas and Clements ,1990; Singhatat ,1991;Clements and Ellerton,(1999 cited in White, 2005).

 

Read the whole article here.  It is well worth it!

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St. Patrick’s Day Glyphs

Posted on March 15, 2011. Filed under: Classroom environment, During the Guided Math Lesson, Elementary math, Manipulatives, Math Centers | Tags: , , , |


Glyphs are a great math activity. Remember they are a pictorial form of data collection (according to mathwire).  Here is a leprachaun glyph

Here is another one.  And another one!

Be sure to see the other posts on glyphs in this blog!

Happy Mathing,

Dr. Nicki

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St. Patrick’s Day Math: Great Activities to Do in Guided Math Groups

Posted on March 11, 2011. Filed under: Assessment, During the Guided Math Lesson, Graphic Organizers, Guided math, Manipulatives, Math Centers | Tags: , , , , , |


The New Common Core Math data standards say that students should be able to classify objects and count the number of objects in each category as well as represent and interpret data.  So here are some great St. Patrick’s day data links:

Lucky Resource 1 (scroll down to lucky charms graph)

Lucky Resource 2 

Lucky Resource 3   (great site for differentiated lesson plans)

Lucky Resource 4

Lucky Resource 5 (graphing in action)

 Lucky Resource 6

Lucky Resource 7

Lucky 8

Happy Mathing,

Dr. Nicki

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Elapsed Time Rulers: Great Guided Math Opportunity

Posted on March 8, 2011. Filed under: Elementary math, Graphic Organizers, Guided math, Manipulatives | Tags: , , |


Students struggle with telling elapsed time.  Elapsed time rulers definitely help!  I suggest starting with stories from hour to hour and then scaffolding it by the half hour and then by 15 minutes and then by 1 minute.  So, this site has several different rulers to do that (you have to scroll down to Other and then Look for TIME to find the rulers).  Here is another great elapsed time ruler and lesson.  Here is one more.  Try them and let me know how it works!

Happy Mathing,

Dr. Nicki

P.S. LOOK AT THESE TIME ELAPSED RULERS

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