Good Morning, Chairman Huffman, members of the Ohio House Rules Committee, and guests. Thank you for this opportunity to meet with you today and to speak against the passage of House Bill 597.
My name is Linda Gojak.
I direct the Center for Mathematics and Science Education, Teaching and Technology at John Carroll University and have done so since its inception 16 years ago. The Center’s mission is outreach to teachers in urban and high needs districts to support their work in offering their students mathematics and science education of the highest quality.
I am the immediate past president of the National Council of Teachers of Mathematics, the national professional organization with over 80,000 members including mathematics teachers ranging from Pre-kindergarten through graduate school. NCTM is not a union. It is a professional organization for thoselooking for and providing the most current research-based information on what it takes to implement mathematics instruction of the highest quality for their students. Membership of NCTM includes classroom teachers, mathematics educators, mathematicians, and mathematics education researchers.
I have also served as the president of the National Council of Supervisors of Mathematics, the Ohio Council of Teachers of Mathematics and the Greater Cleveland Council of Teachers of Mathematics. I have served on the Mathematical Sciences Education Board at the National Academy of Sciences in Washington, DC and currently sit on the executive committee of the Conference Board of Mathematical Sciences in Washington, DC.
Most importantly, I spent 28 years teaching elementary and middle school mathematics in Northeast Ohio. During that time, I received the Buck Martin Award from the Ohio Council of Teachers of Mathematics for outstanding classroom teaching, the Presidential Award for Excellence in Mathematics Teaching (the first Ohio elementary recipient) and the Christofferson Fawcett Award for leadership in Mathematics Education in the state of Ohio. I am a graduate of Miami and Kent State Universities. As you can see I have invested most of my life as a learner and as a teacher in Ohio Schools and working with Ohio’s children.
I speak to you today from the perspective of an experienced elementary mathematics teacher who still actively works with teachers and students in striving for the very best mathematics education we can provide for our children.
Standards are not new to me. I was the K-8 teacher representative on the authoring team of the first set of Ohio’s mathematics standards (Ohio’s Mathematics Education Model) and was deeply involved in helping to prepare teachers to teach those standards. That was in the early 90’s. It is now 2014, and we know a great deal more than we did then about how children learn mathematics. Despite claims that the Common Core State Standards are not research based, it is a fact that some of the most prominent mathematicians and researchers in mathematics education were involved in writing the common core standards including Doug Clements, Deborah Ball, Deborah Hughes Hallet and others too numerous to name at this time. The Common Core State Standards incorporate what we know about how children learn as they define what students should know and be able to do at each grade level.I would like to repeat that. The Common Core standards define what our students should know and be able to do in mathematics to be career and college ready.
They do not dictate a curriculum or a particular way of teaching (pedagogy).
They do notcall for a particular assessment.
They do not tell us how our teachers should be evaluated.
That is up to state and local control.
The content standards and standards formathematical practice dodescribe what it takes to be a good problem solver and to think mathematically. To solve problems is one of the core reasons we do mathematics!
Some have expressed concernthat the standards are not developmentally appropriate, especially at the elementary level. Interestingly, that complaint does not come from knowledgeable mathematics education practitioners who work with children on a daily basis (i.e., classroom teachers). In fact, most elementary classroom teachers who are prepared to implement the Common Corerecognize that they are very much aligned with what young children are ready to learn.
I would like to spend the rest of my time sharing personal examples of the enthusiasm of children learning mathematics in classrooms of teachers prepared to implement the common core standards so the math makes sense and is exciting rather than a series of rules to memorize.
Let me give you a lens on what a classroom that is implementing the common core content and practices looks like. Students in grade 5 are beginning their work on addition of common fractions with unlike denominators. (In grade 4 their experience was limited to adding fractions with common denominators such as 3/8 + 4/8.) The teacher presents a problem. It could be a word problem or a problem with just numbers. For example, the teacher writes
on the board.
Students have an opportunity to discuss what this problem means and predict an answer. From my experience, students respond “. (Even those who have learned to add fractions using a traditional algorithm say this without pause.)
The teacher follows with a powerful question. “Is your answer reasonable? Does it make sense?”
Students continue with a discussion about the meaning of these fractions and what would happen when they were added.
The classroom conversation might sound like “Well, we have a fraction that is more than ½ and we are adding it to ½ so the answer has to be greater than one.”
Another students might say, “Wait a minute, 3/5 is only a little more than ½ so it cannot be right.”
Following similar experiences students are now ready to learn and understand what happens when they add (or subtract) fractions including what is similar towhole number operations and what is different (an example of the connections called for by the Common Core). This example describes howgiving students time to make sense out of mathematics supportstheir understandingand application ofa concept to a variety of situations.
Let me take you into a kindergarten classroom.
The children in this class are exploring the concept of 5. They are working beyond simply counting to 5. They are linking cubes of [FB1]different colors to show various ways 5 can be put together and taken apart. Some may show 3 red and 2 blue and other may show 1 red and 4 blue. They record their work by coloring squares on graph paper to represent their ideas with pictures. [FB2]While this may seem trivial to us as adults, these experiences form the foundation for learning basic math facts, and for future work with addition subtraction, multiplication and division. Students who do not have these experiences are more likely to struggle with important mathematics concepts in later grades.
If you read the Common Core carefully, it calls for students to represent early concepts using materials and drawing pictures. This is not pedagogy. These kinds of experiences are based on what we know about learning development of young children from the work of Jean Piaget. We start with many experiences using objects and eventually move to pictures before introducing abstract symbols, such as the digit “5”. Concrete objects and pictures are fundamental ways that young children understand a concept such as “five.” The use of abstract symbols at the kindergarten level is limited in the common core and recommended only when children are ready.
How many of you have heard someone lament, “I was never very good at mathematics?” I hear that a lot! And, to me that is just not good enough for our children. We cannot continue with business as usual – teaching through rote understanding and rules that are only memorized. We lose too many children who have the potential to do well in mathematics, and thus we close many doors to future careers.
The Common Core State Standards give us the opportunity to have students understand and be successful in mathematics. I have watched students go into high-stakes testing situations with stress and anxiety when they have been taught mathematics as a series of algorithms, rules and steps with no deep understanding. I have a vision of students lugging their figurative “bag of math rules and tricks” into testing situations,and they dig through that bag as they try to remember the rule that works for each test item. They confuse the rules and the steps because they do not understand them orhow to apply these abstract ideas. They havenot developed a deep understanding of what the mathematics means. To be truly prepared to do the work called for in the 21st century, whether in a STEM field or in the work of everyday life, students must be able to reason about the world around them. The Common Core State Standards in mathematics callfor understanding and reasoning to be a part of each child’s mathematical education. We cannot afford to miss such an opportunity.
Thank you for your attention.
[FB1]This 2 is easily confused with one of the addends to 5.
[FB2]Probably not worth the space to explain what a “five frame” is.