From more than 50 years of teaching experience, I鈥檝e learned that elementary school teachers are typically more comfortable teaching reading. They delight in watching students become readers. They enjoy students鈥� rapt attention when they read books aloud to them. They love discussing the ideas that books inspire. They have a variety of teaching strategies and ways to organize students for reading instruction.
I鈥檝e also learned, sadly, that when it comes to math, the same qualities don鈥檛 always exist. Teachers often tell me that they come to math with a combination of trepidation, fear of the subject matter, and a general 鈥渦ncomfortableness.鈥� A sense of confidence is often missing from teaching math, as are feelings of joy and delight.
Math time is often serious and tense. Rigor and seriousness are essential, but so are the excitement and creativity that teachers generate when teaching language arts.
Of course, in some important ways, learning to read and learning math are different. One disparity became clear to me while reading a novel on an airplane. Several times I came upon words that were unfamiliar. Still, I kept on reading and didn鈥檛 get lost. Even if I had been home, I doubt that I would have checked a dictionary. Most likely, I would have continued reading and still made sense of what was going on. But in math, if you miss one blip in class, you fall off the learning ladder. You have to back up and start again to pick up the piece you missed. That鈥檚 the way math is鈥攜ou can鈥檛 skip a step and stay with it鈥攚hereas in reading, it鈥檚 possible to continue and let the context of what you鈥檙e reading carry you.
Similarities do exist between learning to read and learning math. For example, both involve skills. But this similarity also leads to another difference: For reading, there鈥檚 one gatekeeper skill, decoding. While decoding alone isn鈥檛 sufficient for reading proficiency, it鈥檚 the essential skill that gives readers access to the entire world of printed matter. Unfortunately, this isn鈥檛 the case for math. As early learners, children learn to count and add and subtract small numbers; next, they learn about place value and working with greater numbers; then they move on to multiply and divide. They do all of this first with whole numbers, and then face fractions and decimals and how to add, subtract, multiply, and divide them as well. In math, there鈥檚 no one gatekeeper skill that students can practice and perfect: The concepts and skills build and build. It can be daunting.
But other similarities exist. For example, when a child is learning to read, everybody knows that reading proficiency is all about bringing meaning to the printed page. I can 鈥渞ead鈥� anything in Spanish, since I鈥檝e studied some Spanish, yet still not understand much of what I鈥檓 reading. I can 鈥渞ead鈥� about string theory, yet not fully grasp the concepts. No one finds it acceptable to think of a child as a proficient reader if he or she can pronounce the words but doesn鈥檛 understand the material. Comprehension is the key to being a successful reader.
The same standard should hold true for math. If children have memorized the math facts and can perform computational procedures, teachers often think of them as proficient. But we鈥檝e seen over and over again how children can borrow, carry, bring down, or invert and multiply without understanding why the procedures work or how to apply them to problem-solving situations. The standard for math should be the same as the standard for reading: bringing meaning to the printed symbols. In both situations, skills and understanding must go hand in hand. The challenge is: How do we help students develop meaning and make sense of what they do?
A few years ago, when I was leading a professional-learning session at a school, I asked the teachers to list what they thought was important in their instructional program for reading and language arts. I had them do this first in small groups, and then we went around the room and I recorded as each group reported something from list. Here are some examples of what they said:
- We want our students to love reading.
- We want them to develop good word-attack skills.
- We want them to read fluently.
- We use a variety of teaching strategies鈥攕hared reading, guided reading, independent reading, read-alouds.
- We include comprehension from the very start.
- We ask children to make predictions about what might come next in a story.
- We do a lot of making inferences.
- We want students to decipher meaning from contexts.
- We ask them to pose questions about what they鈥檙e reading.
- We want them to identify what鈥檚 important and what鈥檚 not as important in what they read.
The standard for math should be the same as the standard for reading: bringing meaning to the printed symbols.鈥�
After we had gone around the room several times, and I had filled two sheets of chart paper with their ideas, the teachers were still excited. They had a lot to say, and they radiated enthusiasm.
I then said, 鈥淟et鈥檚 review each statement, change the reference from reading to math, and see what we discover.鈥� Doing this made some of the teachers uncomfortable. Some admitted that the focus on comprehension and thinking skills that was so prevalent in their language arts instruction was missing from their math instruction. Others noticed that the confidence they felt in articulating what they did during reading instruction didn鈥檛 exist when describing their math instruction.
We had an interesting conversation about the relationship between fluency in reading and fluency in math. While comprehension was key to reading fluency, with math they often felt relieved when students could compute accurately. One teacher commented, 鈥淪ometimes I know that students don鈥檛 understand why they are borrowing or carrying, but I don鈥檛 know what to do.鈥� This experience was a start for us to discuss essential questions about math instruction: What are your beliefs about teaching math? What are your goals for the students?
A major challenge at the elementary level is teachers鈥� content knowledge. Most teachers don鈥檛 have the same content knowledge in mathematics that they have for reading and language arts. I鈥檓 convinced that you can鈥檛 teach what you don鈥檛 understand, and I think that learning more about the math they have to teach is an important area for teachers鈥� professional learning.
But, just as I know that children learn best when they connect new learning onto their existing knowledge and skills, the same holds true for teachers. How can we connect literacy and math, so that teachers bring the strengths they have with language arts instruction to their math teaching? How can teachers make links between mathematics and language arts pedagogy that will enable them to engage children with math in the same way they bring children to the wonder of reading?
One way is for teachers to think about leading classroom discussions in mathematics as they often do when teaching language arts. Probing students鈥� thinking during math lessons is valuable, so that the goal is not only getting correct answers, but also explaining why answers make sense.
Teachers typically ask students to explain when they鈥檝e given an incorrect answer. 鈥淎re you sure about that?鈥� is often a signal to students that their answer is wrong. But it鈥檚 important even when their answers are correct to ask: 鈥淲hy do you think that?鈥� 鈥淗ow did you figure that out?鈥� 鈥淲ho has a different idea?鈥� 鈥淗ow would you explain your answer to someone who disagreed?鈥� It鈥檚 useful to have students comment on their classmates鈥� answers as well, asking them to explain what a peer said in their own words, or asking students if they have a different way to explain the answer. If students are stuck, it鈥檚 sometimes useful to have them turn and discuss the problem with a partner and then return to a whole-class discussion.
Instructional practices like these support the development of skills and help students cement and extend their understanding.
There鈥檚 much for us to think about to help teachers teach math more effectively. But I think we can make headway if we take the two most important areas of the curriculum鈥攔eading and math鈥攁nd look at them side by side to analyze what鈥檚 the same, what鈥檚 different, and what we can learn from one to enhance the other.
