July 2, 2019

This image best exemplifies the difference between equality and equity, give everyone the same size bike vs give a person a bike that best fit their ability. In education, we tend to give students all the same information, assuming they are all at the same level and expect them to learn and progress at the same rate. In reality, students come to school with very different experiences in math. Some students come well prepared, their parents played Raffi or Trout Fishing in America songs in the car, songs that consecutively increase or decrease in number like Numbers Rhumba or 18 Wheels on a Big Rig. Their parents had books and games available to them. This isn’t the case for a large number of our students, “Children from some groups come to school with fewer experiences in mathematics.” They come to school without the basic foundation of sequential counting. They don’t understand one on one relationships between a quantity and a number. “For too many, these differences do not disappear. The achievement gap has its origins in the earliest years, with low-income children possessing less extensive math knowledge than middle-income children of pre-K and kindergarten age.” D Clements and J Sarama, Kennedy Institute for Educational Success.

“The myth that math is a gift that some students have, and some do not, is one of the most damaging ideas that pervades education in the US and that stands in the way of students’ math achievement.” Jo Boaler , professor Stanford University. According to Ginsburg, Herbert P.; Lee, Joon Sun; Boyd, Judi Stevenson in an article with Society for Research in Child Development "Cognitive research shows that young children develop an extensive everyday math and are capable of learning more and deeper mathematics than usually assumed." Infants are tested on number recognition to prove that quantity is an innate concept. A concept, that with nurturing and guidance, can grow. Students do not differ in their ability to grow to learn. They simply differ in experience, expression and learning styles.

I’m a prime example of this, I have a learning disability, dyslexia. I didn’t struggle with the algorithm; I could follow a pattern. What I struggled with is number sense and applying that numbers sense to math problems presented in a story problem format. Reading a problem and figuring out what numbers and operations I should use was a HUGE challenge. Teachers would explain it on the board showing an example, but when I had the paper in front of me and had to decipher what was important on my own, I continually failed. I know now that it doesn’t mean I’m bad at math, just means they didn’t present the information in a way that I could understand it or that allowed me to use strategies that helped me best process, apply and retain the information.

I can’t express this enough, YOUR ATTITUDE TOWARDS MATH MATTERS!!!! I don’t care if you hate math with the heat of a thousand suns. Do NOT let your students, children, family, anyone know. Johnny isn’t bad at math because you are bad at math. Johnny is bad at math because he is told that math doesn’t matter and “I’m not a math person” is an easy way out.

I get it though, there is an intimidation about math, we feel like there is a requirement to process math quickly and if we can’t we are a failure. This isn’t true. Math is about thinking, so take the time to think. Think it through with your student. You don’t need to know the answer to the problem, have a curiosity to help find a solution to the problem. Talk it through and don’t feel stupid if the answer is incorrect, brain development happens when incorrect answers are recognized and learned from. So, laugh off errors and try again! This also role models persistence, a necessary quality.

Working with kids in math, especially those who haven’t found success with it or who didn’t have the early math experiences have to be taught to keep a positive mind set. Start by helping to teach kids to change from an I can’t, to an I can attitude.

- Teach Positive Talk: We need to teach the students that they can succeed. Repeating things like “I think I can, I think I can” until they can. Brains can develop and grow when they are worked and challenged. Talking positive and pushing oneself helps to build that stronger brain. There is also a theory that you can change your attitude by changing your body. Standing in a “Superman” pose sends endorphin and testosterone throughout your body telling it’s got this, even when your head is saying “I’m not sure.” It’s a theory called “fake it til you make it”. Spending one minute of class time in a positive pose can have great effects on student’s belief that they can do it. Students can have a negative reaction to being told how to think. Don’t go around saying “you just have to be more positive” or “you need to try harder”. Both can backfire. Model positive talk, “I’ve got this”, “you’ve got this”. Be the group cheerleader!
- High Expectations: It’s proven again and again, if you set high expectations your students will rise to meet them. Letting your students know that you have faith that they can succeed often gives them the push they need to try harder. But if a child should fail, there is no judgement placed on the child. They know what they did is incorrect, help them learn from their mistakes by going over the problems together. Mistakes are proof that a student is trying. What we miss so often is the review of the mistake so that they can learn from it.
- Repeat, repeat, repeat: to learn a new habit or behavior and make it automatic takes 66 days or 9 ½ weeks. If school starts on Sept 1, it would take until about Nov. 5 before that behavior becomes automatic with some students. With students that aren’t at school every day or have a home environment that doesn’t reinforce the new behavior, or they have a learning disability, it can take the entire school year for that behavior to become automatic.

Students in any classroom differ in many ways. Some differences will be cognitive, what previous concepts and skills students have learned. Some differences will be more about learning style e.g., whether the student learns better through auditory, visual, or kinesthetic approaches. Other differences will be more about preferences; including behaviors such as persistence, inquisitiveness and personal interests.

Creating a differentiated lesson does take time, time we often do not have, so how can we make it simple. According to NCTM, there are three elements to think about and I’m adding a fourth:

- Big Ideas – What is the focus? What is the concept are we trying to have the students understand? Not necessarily the specific skill but the overall math concept. For example, the content should not be a strategy on addition of multi-digit numbers, but the concept of adding or joining things that are alike. Students can work in various stages along one big idea.
- Prior assessment – I know there is a lot of talk about over testing our students but that is when the assessments do nothing to provide data from which to work. Doing a quick written or oral assessment of students will help determine where to start.
- Choice – research suggests that giving students voice and choice a minimum of 35% of their time in class will increase their motivation to learn. Adding choice to a class is fairly easy. Some students may choose to quietly work on their own, others may choose to collaborate and communicate with others, some may choose to do a deep dive. Providing a once or twice a week choice allows them to feel more in control of their own learning. Choice can also be in the form of various games or activities that teach the same concept and students select which game or activity they want to do.
- Summarize often - you personally don’t have to summarize, have the students explain what they just learned, have them communicate and defend their thinking. Not all students want to do this to the large audience so provide quiet moments to have students speak to you one on one. Math is not a spectator sport, you must get in there and talk, listen and grow.

When thinking about equality vs equity ponder over how you approach math yourself. Think about your preconceptions and biases. You don’t have to have all the answers. We can all grow together. MANGO Math is here to help as well. I developed the curriculum to be an easy way to approach math with students of various abilities and experiences. If you have any questions, please feel free to reach out and together we can find solutions.