Years ago, Steve marveled at how 15 one-hour tutoring sessions allowed him to address more than he ever could in 180 50-minute Algebra 1 classes. He didn’t just cover the math, but instead, he was able to teach it with far more understanding and achievement. More recently, Caroline has experienced how weekly 45-minute tutoring sessions with struggling middle schoolers has improved self-confidence, elevated attitudes toward math, and raised achievement.
When we compared notes, as grandfather and granddaughter, we were struck by the overlap in our practices and the way we both attributed our success to these practices. Here are three practices that we believe undergird effective tutoring.
1. We work to build personal relationships with those whom we tutor.
We understand that one-to-one tutoring gives us opportunities to build a close, working, and personal relationship that is impossible to develop with a 1:25 typical teaching ratio. For example:
- Too often, those whom we tutor feel left out in school; they aren’t convinced they belong and are embarrassed by their cognitive obstacles. They struggle to connect with others. Enter the tutor who asks about their interests, their siblings, and what makes them happy – all as part of building a caring and collaborative relationship.
- Since mistakes are an inevitable part of learning mathematics, a strong personal relationship is needed to reduce fear and embarrassment about these mistakes. This approach also helps turn errors into powerful learning opportunities.
2. The heart of effective tutoring is the questions we ask.
We as tutors learn far more about our students and their learning processes, and our students learn far more about math, when we ask questions and wait for answers, rather than from merely talking and showing. For example:
- As tutors, we always hear ourselves asking questions like “Why?”, “Can you convince me?”, “How did your brain picture that situation?”, and “Can you explain that to me?” Questions like these, should be asked frequently, after receiving both correct and incorrect answers. Such questions engage those we tutor in the thinking and reasoning that supports real learning and understanding.
When plan our tutoring sessions, we pay as much attention to the questions we intend to ask as we do to the tasks we present. Questions like “Why did you multiply instead of divide?” or “How would you convert centimeters to meters?” help us focus in on key understandings.
3. Our go-to strategy is focusing on alternative approaches and multiple representations.
We understand that students process mathematics differently and picture or visualize mathematics differently from one another and from us.
There can be no one-size-fits-all approaches.
In fact, one of the most common reasons that students struggle with mathematics—and can benefit greatly from tutoring—is that their brains see and make sense of the math in non-traditional ways, requiring us to consistently suggest different approaches and different ways of visualizing the math they are learning in an ongoing search for the right cognitive fit. For example:
- Consider a student struggling to remember the sum of 8 and 9. Many times it seems that all the practice in the world doesn’t seem to cement this fact into memory. Perhaps it’s time to recognize that the neural connections that link 8 and 9 to 17 just aren’t there and can’t be coaxed into existence. Our approach is to ask how else might this student retain or derive this fact. We talk about and model doubles plus one (8 + 8 + 1 = 16 + 1 = 17) or we discuss replacing 9s with 10 and then subtracting one (8 + 9 = 8 + 10 – 1 = 18 – 1) or using tens frames to visualize 8 + 9 as 10 plus 10 – 2 – 3).
- Consider the middle or high school students struggling with adding and subtracting signed numbers such as finding 5 + (-9). Instead of memorized rules that make little sense to most students we turn to football plays and ask students to visualize gaining 5 yards on the first play and then losing 9 yards on the second play to see how losing 5 takes you back to the start and yet you have 4 more yards back to go to get to -4. Or remember that for some students, the horizontal number line is not a friend and their brain sees up and down better than left and right. For these students we turn to above and below sea level, or thermometers or elevators to visual signed numbers. And sometimes it’s a simple matter of helping those whom we tutor to consider starting with $5, but owing his or her mother $9 to see that 5 + (-9) must equal -4.
For lots more detail and ideas about effective tutoring we urge you to take a look at our The Math Tutor’s Handbook: Strategies and Tips for Success published by Corwin.
