I am currently in the unit of Parts to Whole, teaching bar modeling. Looking ahead, it seems to me that bar modeling is a big part of not only this unit but upcoming units as well.
My wondering and question: I have students who are looking at the problems and can figure them out by stacking numbers then using the renaming strategy which was what they learned in lessons before bar modeling. Should I be encouraging all of my students to draw the bar model before stacking the numbers to solve the problem? How critical is it for them to bar model? Please know that I am not saying that I don’t want to teach it at all, but I don’t know how much I should be “pushing” those that either don’t understand it or those that feel like they can work the problems using other strategies.
Learning Math Facts
Math facts are simply the basics: addition, subtraction; multiplication; division. They are basic number combinations and calculations we do every day. So why is it that learning math facts creates such huge problems for teachers and students in our classrooms?
Common subtraction mistake when children are learning math facts.
Is it that some of us are just naturally better at math than others? Perhaps. The good news is you as a teacher can help anyone improve their math skills. You might be wondering how. Well, rote memorization alone won’t get us there.
Many teachers ask how to help students record the renaming process in the addition algorithm. What language should I use?
I learned to “make trades” or “borrow” when adding and subtracting that require renaming. Is this still correct?
How can we help students understand conventional methods?
How can we differentiate instruction without putting more work on our plate?
Teachers do not have time to prepare multiple tasks and lessons to meet the needs of each student in the classroom. The key is giving an anchor task that all students can enter and knowing how to adjust the task based on our observations.
In this class, students were guided to use “Katell’s” method (aka-left to right strategy) to solve the problem 65 – 12. Notice how the student recorded their thinking process.
How can we differentiate with one task?
During the guided structure component of the lesson, teachers are observing and questioning students. This student demonstrates and can explain the left to right strategy. What comes next for this student? During our planning phase, we need to ask ourselves, “What can I do for the student that already knows the answer”? Looking at this student’s work, how can we deepen the mathematical understanding?
After listening to the student explain his thinking, the teacher commented, I can understand your verbal explanation, but your written work is confusing to me. I wonder why I am confused? The teacher then walked away, and the student grappled with the idea of equality. Differentiation is meeting the student where they are at and extending the learning.
Do not try to create more problems for students to practice. Plan your task thinking of what mistakes students typically make and how you can help extend the thinking. Use your observations to go deeper and differentiate!
What are other ways you could take the task 65 – 12 and extending the task? Share your thought below.
How can we help student refocus on understanding versus just an answer?
Too often when we pose a problem and students shout out an answer. We need to ask ourselves do students understand the concept or are they obtaining the correct answer by fitting the symbols and numbers into a structure they know?
In this example, the anchor task was to subtract 34 from 87. The teacher wanted to screen the children first wondering, Do students know what it means to subtract one number from another? To find out more the teacher posted the following problem, removing the numbers.
Do students have the conceptual understanding or just fit the numbers into a given structure?
Students were asked to set up the expression that could represent the situation. The student A on the far right was the only student in the class that seemed to understand. When asked to explain his thinking, many observing teachers felt he understood the concept and that he gave us a platform to generate a discussion.
Do students understand the part-whole relationship here?
Following this analysis, the numbers were inserted into the problem. Subtract 34 from 87. It was interesting to see student A’s work. Much to our surprise, Student A who seemed to understand the concept had a hard time transferring that knowledge to another situation. Notice his equation is not correct but he gets the final answer.
Can student A transfer knowledge from one setting to the next? Look and listen to help guide students to conceptual understanding. Looking at answers does not tell us the whole story.
Less is more. Spend more time on conceptual understanding and listening and watching students versus solving more problems. The answer does not help assess student reasoning or how we can extend or guide the learning process.