I watched a technician in the auto shop balancing and installing new tires on my car. He used a pneumatic wrench to tighten the lug nuts that secure each wheel to its axel hub. The sound of the wrench ratcheting said the nut was tight. When all four wheels were attached, he walked around the car and manually checked each with a torque wrench.
Catching my watchfulness out of the corner of his eye, he said “Just making sure the work is done right. Don’t want your wheels flying off while you are driving”.
What We Should Know
With my car safely back in the school parking lot, I recently watched fifth grade children struggle with dividing fractions. The concept of a reciprocal, inverting the divisor, and multiplying the dividend by the inverted divisor is a head scratcher to many children. Dividing fractions is not a single lesson, but an operation that is taught, clarified, and strengthened in many lessons. Some children demonstrated they understood but others had no confidence in their work. They did what they were told to do without understanding why they did it.
Over the next weeks, I observed this fifth grade teacher checking the lug nuts of dividing fractions. She knew that only a few children successfully learned this operation through their initial instruction. Consequently, she literally walked new and clarifying lessons on dividing fractions around the classroom until every child knew what to do when presented a fraction to divide and also could explain how the reciprocal of the divisor allows us to use multiplication to split the dividend into equal parts. She made each child’s future division of fractions roadworthy for use in learning advanced math.
Does this make teaching and learning just a matter of mechanics? Not at all. It demonstrates the diligence required to ensure that all children achieve learning success. Knowledge and skills that are essential for future and scaffolded learning require teachers to check and recheck that these have been securely learned by every student. Without the process of checking and tightening, the wheels of their future education will come loose and their learning will crash.
Why Is This Thus?
Although I use mathematics as my example, this blog applies to every unit of instruction taught in school.
The legendary math “wall” is real and almost all students hit their math “wall”, usually within the content of trigonometry or calculus. The “wall” arrives when the abstraction of mathematics is greater than the student can conceive. The “wall” is not a big deal because most of us do not use advanced math in our daily living or careers. However, not having the math skills below the wall is huge. All children need to be skillful in math reasoning using numbers and operations, measurement, data analysis, geometry, and solving problems with unknowns. These are career and life math skills.
https://nces.ed.gov/pubs97/97885.pdf
Successful learning in math up to the “wall” is achieved through scaffolded, grade level or course instruction, and active engagement between a teacher and student. The scaffold looks like continuous instruction in 4K through grade 6 mathematics, pre-Algebra, Algebra 1, and Geometry. The scaffold is an annually spiraled teaching of operations, reasoning, and problem solving. Each successive instruction tightens student comprehension and application of math learning.
Active engagement is when a student interprets the math problem, explains her plan to solve the problem, uses math thinking and reasoning to resolve the problem, and presents a solution. Engagement is all of these, not just one of the three. The process takes in-class time because it requires ongoing student and teacher conversations. The student must put math into words and words into mathematical thinking and use mathematical thinking to find clear and clean solutions. The teacher listens, critiques, guides, and confirms. The conversation is a must because it clarifies and secures the student’s learning. The conversation is the teacher’s torque wrench.
We tighten the math lug nuts in 4K through algebra/geometry by actively engaging each student in exercising their mathematical reasoning continuously through the math curriculum.
What Should We Know About This Thusness?
It is easy and fun for teachers and students to start new lessons. Motivation to do the work assigned is high when the information and skills are being introduced. There are multiple “I get it” moments. As the applications of the new information and skills become more complex, the number of “I get it” moments are harder to achieve. Ultimately, more students say “I don’t get it” and this is when the engagement between teacher and student is critical.
“Tell me what you do get” starts the conversation of clarification.
“Let’s rethink the problem” opens new possibilities for successful learning.
“Let’s assure we are applying the right operations in the order needed and that we understand why we are doing this” secures student learning.
Each of these steps is an out loud conversation that moves a student from “I don’t get it” to “I get it” and the ability to apply what is learned in the future.
It is the diligence to complete and secure student learning that is hard and this is where too much teaching and learning stumbles. The wheels come off a student’s learning when we leave her in an “I don’t get it” moment.
To Do
Plan what the learning outcomes look like and secure the learning of each outcome for every student. Tighten the lug nuts everyday.
Do this through personal engagement. Asking “Are there any questions?” after giving students initial instruction only confirms that no one wants to ask a question. It does not confirm that any student learned what was taught. “Does anyone have a question?” does not tighten the lugs.
“Tell me…” and “Show me…” and “Explain your thinking” and taking the time to listen, clarify, critique, and confirm are the wrenches that tighten the lug nuts of student learning.
The Big Duh!
Because there is so much to teach and so little time to teach all of it, we feel the need to move quickly through units of instruction. “We need to be done with this unit by the end of the month” often drives us to close the unit before all children are secure in their learning. We are consoled by the curricular spiral and thinking “if they don’t learn it this year, they will learn it next year”. This is how the lug nuts of learning loosen. Next year’s learning is predicated on success this year, it is not a repeat of the past.
Don’t worry about how long it takes to have every student reach secure learning of a unit. Learning is built upon secured learning; future learning fails when the clock tells us to move on.
Tighten the lug nuts of learning in every lesson taught to ensure all students are roadworthy for their next educational adventure.