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Carol Knight 
knightcj@pwcs.edu 

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Donna Stofko,  stofkoda@pwcs.edu

Linda Zborofsky, zborofln@pwcs.edu

(703) 791-8849

 

 

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Investigations
in Number,
Data, and Space

 

Evidence of Success with Investigations

         Testimonials
            Testimonials will be changed regularly.
      Please share your success stories with us by sending an e-mail to the PWCS Office of Mathematics.

I was attending my son's winter banquet at OPHS last night and I happened to watch a little boy (3rd grade) doing his math homework. I asked his Mom if it was Investigations...she said yes. Then I asked if she liked it and she said that she LOVED it!!! She said that he is solving problems in all kinds of cool ways and (here's the best part!!!) that he already knew his times tables better than his older brother (in 7th grade). Hooray!
 


Minnieville students draw quick images as one of several Classroom Routines.

I have been using Math Investigations for three years now at the first grade level (since before it was officially adopted as a text).
My experience has been extremely positive. My students all look forward to learning math, they have better number sense, and they are better able to problem solve. They also are better able to articulate what they are learning and to write about how they solve problems. 
Just a quick note to let you know how much I enjoy teaching Investigations and how much the children are learning. Yesterday and today we worked with the Crayon Puzzles. I thought these would be quite difficult for my children - but, to my surprise, they UNDERSTOOD and did amazingly well!  I was just delighted and wanted you to know that I can see how the children are really coming to a good understanding of the Math concepts presented. They love Investigations and I look forward to beginning each day with these fun and exciting activities. We are definitely noisy, but VERY involved and focused. Thanks for finding this series for us. One thing we have found interesting with the complaints this year is the comments about gifted students. Our gifted kids are doing very well. Investigations is like Montessori school for them they can tailor it to their needs  and interest. I have two kids that are in START that could help Investigations sell their materials. Actually we are finding it is our ESOL kids that need more support. They sometimes need support with explaining how they got an answer. We feel it's very important for Our ESOL kids to get support in Math as well as Language Arts. It makes a very positive difference for them.


Cedar Point Kindergarteners play
Racing Bears

The difference between my current students who were exposed to Investigations and the students who were never exposed to Investigations is phenomenal. Students come with understanding and prior knowledge and use this understanding and knowledge to build more meaning and assimilate new information. Students now come to math with an understanding of the base ten system. They know and say that “42" is 40 plus 2 more, or 4 tens and 2 ones, or 38 + 4, or 10+10+10+10+2, or 45 - 5, or a quarter + a dime + a nickel + 2 pennies…and on and on and on…the possibilities are endless. They can count off-decade with understanding that ten is being added each time. Learning is not rote, remote, or meaningless. It is instead meaningful and relatable. It is evident that students have learned that there are many ways to reach a solution. In contrast, some of the students that were never exposed to Investigations, lack basic understanding of how numbers relate and have challenges with decomposing, adding, subtracting, multiplying and dividing numbers. They say 42 is 4 and 2, and find it challenging to solve problems in inventive ways. They mostly see the canonical place value of 42 – which is 40 + 2 (4 tens + 2 ones); and that is still without the understanding or exactly  how many is “40.”  When asked to add 42 to another two-digit number they find a solution that has 4 digits. The meaning of the numbers is not there and so they are not able to apply basic concepts to more challenging tasks.  All of my students that use Investigations are showing improvement in number sense. They are able to logically solve problems. Numbers now have meaning and this meaning is applied to different concepts. Students are able to communicate mathematically. They can prove, justify, reason and debate solutions. They have opportunities to learn from each other and also to learn to be accountable for their own work. They have become risk takers -  challenging themselves and others. Their curiosity is limitless. Investigations has helped our students be more successful in math. Over time, I believe that the data will speak wonders!  It seems logical that if students’ math understanding increases, then the end products (i.e. CFA, SOL) scores will also show improvement.  


Antietam students practicing combinations of 10

I am a first grade teacher at Triangle Elementary and I am a parent of three PW county students. My youngest son is a third grader at Marshall elem. He has had Investigations every year since Kindergarten. I told our math specialist my story about him and she suggested I pass it along to you. My son is an average student. The other night we were working on his homework and he wanted help for a subtraction problem. I began to do the algorithm and he said, "Mom, you know it has to be around 54....just add 54 to the bottom number."  When I did, he automatically noticed we were 10 over and said,  Oh, it is 44!" I was amazed to see how strong his number sense was and how easily he moves between addition and subtraction. He has recently began to do multiplication and division and he is equally flexible with these types of equations. I know that there is a lot of controversy, but as a teacher and a parent, I have seen the benefits of giving the students a strong number sense. These students will be able to know right away if their answer even makes sense.

Thank you for letting me share my little story.
Yesterday, in the car, I asked Kyle (2nd grade), "If you had to read 3 chapters a day for the next 4 days, how many chapters would you read?" He paused (shortly) and then replied, "12". 

I then asked, "How did you come up with that?" His reply was, "If 3 x 3 is 9, then 3 x 4 is 12." Now this is from a child who has not been taught multiplication yet, nor the times table. This is all from the learning of the Math Investigations program. I really believe using Investigations as the basics will evolve into "knowing" the multiplication table, but with understanding, not memorization. 

I have to think that the parents having difficulty doing the homework with their kids should step back and take a lesson from their children. Their kids will have a better sense of critical thinking, a better sense on "how to figure out a problem", whether or not it was mathematical, and a better sense of open-mindedness and have the ability to adapt to new concepts and situations.
Third grade teachers deserve a multitude of praises for working exceptionally hard to ensure this class learns in the new framework. They are working double time, learning the new system themselves, and then teaching it to our children.  I have been very fortunate to have very experienced and compassionate teachers at my child's side during this journey. I attended the TERC summer Institute two summers ago and was very impressed. With a background in child development I can tell you this program makes sense! It allows children to learn by communicating their mathematical thinking and sharing with others their strategies for solving problems. The collaboration piece is so important. While, yes, we agree there is one correct solution, but there may be several ways to reach it. What better way to learn then from one another. When the students get a chance to share their ideas and ways of thinking, everyone benefits. My daughter who is a sophomore and struggling in algebra ll, knows the planning and preparation that goes into implementing this program. Yet she has heard and seen the benefits. She commented to me one day, "Mom, I wish I could have learned math the way your students do, then maybe I would understand it better." And yes, she solves algorithms as she was taught with rote learning, but has no idea why they work! Investigations follows the recommendations of the NCTM. All the SOLs are taught through Investigations as well. That has not changed. What has changed, however, is the brain research on how children learn. Investigations enables all students to experience math in a positive way.  I have been teaching for a number of years and been privy to many different programs and I can say with certainty that this program does work.

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