Math Supervisor Linda Zborofsky,
zborofln@pwcs.edu

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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 offdecade 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 twodigit 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.  

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 openmindedness 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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