Archives for category: Education Reform

bobMuch debate in the field of mathematics instruction revolves around questions like these:

Do we teach for conceptual understanding or procedural fluency? Do we opt for direct instruction followed by application, or do we facilitate as students explore and make connections for themselves?  Is learning multiplication facts an appropriate use of class time?

Literacy instruction has been the subject of a similar debate.  While there are still people who advocate strongly for either a phonics-based approach or a whole-language approach, most progressive educators agree that a balanced approach that combines the best of both phonics and whole language is most effective. I believe that the same is true in math instruction, and that looking to literacy for a model can be helpful.

In reading, the ultimate goal is comprehension–understanding what we read. In math, it’s problem solving–using numbers to represent real world situations. In both cases, students need other skills and proficiencies to achieve these goals.

Learning phonics, or the sounds the letters make both on their own and when combined, is critical for reading success. Similarly, in math, the building blocks are the number system and basic fact fluency. Just like it’s difficult to make sense out of a passage of text if one does not know that “c” and “h” together make “ch” like in “chip,” understanding mathematical situations becomes extremely challenging when one does not know that 9 x 5 = 45.

Understanding and remembering what you’ve read is difficult if you have to stop and sound out every word. This is why teachers model and students practice reading–so it becomes smoother and more natural. In math, using inefficient strategies or relying on clever mnemonic devices to complete calculations diverts attention and cognitive energy and, in many cases, can cause students to lose track of the bigger problem they are trying to solve. That is why building both conceptual understanding and procedural fluency, sometimes through practice and repetition, is important.

In a balanced literacy classroom, instruction focuses on both the nuts and bolts of reading and writing, as well as understanding the big picture. Students are expected to know the alphabet and the sounds letter make. Teachers model smooth expressive reading and help students develop strategies to comprehend what they read. Students practice reading in many different contexts every day. Thinking about mathematics instruction the same way can help students master the skills they need to meet the ultimate goal of using math to make sense of the world around them. Students should learn the number system and their basic math facts. They should develop deep conceptual understanding and practice efficient strategies for calculation. Teachers should model and explain strategies for making sense of problem situations and students should be engaged in problem solving in many different ways every day.

~Bob Dietzen, Math Specialist, City Neighbors Hamilton~

monica pic

In my experience in elementary classrooms over the years, (including in our City Neighbors early grades classrooms and now in a mentoring capacity) I find that about this time of year, the question tends to come up:  “What part should effort and hard work play in children’s schooling?”

Teachers in the classroom are readily able to see that there are two parts to the process of learning something new:  whether the child has the skills needed and whether the child has the independent work habits to apply those skills.  For young readers, there is no substitute for their own independent practice at reading.  Skills are introduced at certain times; there is also plenty of time for practice to apply those skills. Or consider middle schoolers, working to systematically research their year-long project.  A certain amount of industrious trying will lead them to be successful.

At times this can be a bit confusing for families.   Sometimes parents’ reasoning can be:  “We chose City Neighbors so that our child would enjoy school and not find it tiresome, as our own schooling sometimes was.” So when the first rush of back to school excitement is naturally lessened, when some reluctance for working at skills asked of children can come up, parents may become concerned.  “But I want my child to love to come to school…”

Yes, but:  Even if adults love their profession, will they love every minute and aspect of it?  (paperwork or repetitive parts of even a well-loved job?)  For kids’ job as students, there will be some practice and “repetition for mastery” at school, necessary to grow skills.

Research in the past few years about learning shows that those who feel industrious mental effort actually makes a person smarter are more likely to take on difficult tasks, doing well at them.  It is apparent to teachers that how successful children are with mastering skills is in large part related to how well and how long they are able to persevere  working independently—even when it becomes difficult or “hits a snag.”  Children’s  ability to stick with it does not appear to be necessarily related to how “bright” the children are but rather to how much they see themselves as independent people who can work at something until the job is done.

So as parents it helps to praise our kids’ work not with a “You’re so smart” as often as with a “Look how hard you worked at that.” This message is that their effort matters, and will bring a result which is in their control. (And we can encourage “sticking-with-it” skills at home too, with even simple chores like making the bed neatly or organizing or doing a load of laundry.)

My impression from City Neighbors classrooms is this: they do love to come to school! There is a lot of the pure joy of discovery in those City Neighbors classrooms, but also satisfaction of a tough job, tried and completed well!

~Monica O’Gara, Early Childhood Specialist, City Neighbors Charter School~

megan dash picIf I had a dime for every time a parent rationalized their child’s difficulty in math with their own, “but-I-was-always-bad-at-math” story, I’d be able to retire already! Some students find learning math to be difficult because of its concrete nature and building block structure.  Others find it comforting for the same reasons. Overall, children of all ages, grade levels, and genders report hating math. Inside of the classroom, not only do we fight the “I-hate-math” attitude, we continue to fight gender stereotypes about the subject–boys are good at math and girls are not.

Larry Martinek, founder of Mathnasium, wrote, “Children don’t hate math. What they hate is being confused, intimidated, and embarrassed by math. With understanding comes passion, and with passion comes growth – a treasure is unlocked.” (Mathnasium LLC, 2018)

So, how can we change your child’s attitude about math, their “MATH-itude”? Here are 5 easy steps you can take right away:

Eliminate math from the naughty words list.  When talking about math, you don’t have to be overly excited, but it shouldn’t be a curse word in your home. Make your problem-solving and mathematical thinking visible to your child.  Explain your thinking, your challenges, and your solutions. Understanding the process may make the solution seem less intimidating.

Ask for their mathematical assistance.  Students retain math skills best when learned in context. Ask your child to help you solve a real-life math problem to solidify mathematical problem solving and creative thinking skills. For example, how many gallons of paint do you think we will need to cover all four walls in two bedrooms? Why do you think the speed limit decreases when we are going downhill? What is the most efficient way to rearrange the furniture in your bedroom to allow for the most open play space?

Share your love of learning.  When you are excited about learning–not just math–your children notice it.  They seek engagement and modeling. Take mathematical risks and share them with your children.  Invest money, deposit the coins you’ve been saving, try a new recipe but convert some of the measurements as a fun challenge!

Praise them. It’s okay to acknowledge good grades, but we don’t praise grades, we praise people! Ask about and discuss your child’s EFFORT, not their grades. Success isn’t always about the end result, rather the process, which leads to a richer learning experience. When children share their thinking and hear adults praise them, they begin to believe what they are saying is true.

Measure your math-itude.  What kind of message are you sending your child? Identify what is making you confused, intimidated, or embarrassed and acknowledge it out loud. Then actively and openly look for a solution. Be an example of perseverance and embracing the process.

And remember, “If you don’t like something change it. If you can’t change it, change your attitude.” Maya Angelou

 ~Megan Dash, Special Educator, City Neighbors Charter School~

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