Learning happens when it's supported by strong relationships - every student learns differently, and the best for me to learn how to best support them is to ask, and to take student responses seriously. Research supports that, while it is important for students to learn to recall key facts, memorization ultimately is not sufficient for retention of learning or transfer of knowledge to other contexts. I work with students to build understanding beyond memorization of procedures or facts.

I'd first introduce myself to the student and ask them to tell me a bit about themselves. I usually let the student explain to me how they feel about the material in the class, and let them point out the parts that they do and don't feel they understand. I'll ask a lot of questions when they are explaining their thinking about math problems to get a better sense of what mathematical ideas they are confident in. The most important goal of a first session is to build rapport with the student - a positive relationship will support learning and will allow students to feel safer asking questions and sharing creative reasoning (which is often brilliant) about which they're unsure.

In math, becoming an independent learner is closely related to being an independent problem solver. Independent problem solvers are able to work with a problem after they get stuck, and they have metacognitive strategies so that they do more than just stare at or give up on a challenging problem. Many of my students have benefited from learning to ask themselves the questions "what is my goal?" and "how can I get closer to my goal?" when solving algebra or calculus problems - these two questions can help students recognize the ideas and techniques they should apply to a particular situation. As I continue to work with students, we learn more metacognitive problem-solving strategies that support independent learning.

Connecting students with a variety of media for understanding content is important for motivation - if tutoring sessions involve endless writing on the electronic whiteboard, it gets pretty boring. I incorporate programs like Mathematica and Wolfram Alpha into my tutoring so that students can interact with math in other forms, and ask questions that might not be apparent using just video chat and a whiteboard. I also work to build a positive, friendly relationship based on accountability with my students. When I mess up a problem, I say so. If students don't complete a homework assignment, we talk about why. Often, a positive relationship is enough to motivate students to complete work. Making connections to student interests is also an effective way to help students engage.

When students have difficulty learning a skill or concept, there are a number of approaches I can take.

One is to simply explain it a different way - using different diagrams, equations, or pictures or assuming different background knowledge. Sometimes, I check to see whether the student has background knowledge I consider to be prerequisite.

In other situations, it is helpful to create a set of scaffolded questions, leading students to a discovery of the concept themselves. These questions are written carefully to prompt students to see exactly the patterns or structures that we are studying. Often, this is the best way to make a difficult concept understandable - it builds intuition rather than promoting memorization.

This is a great question! I'm mostly a math tutor, so I encounter reading comprehension difficulties mostly in the reading of problems. Often, a good way to start is to ask the questions "what's going on in this problem?" or (more specifically) "what is this problem asking you to do?" If students aren't able to answer these questions, we look for key words "how many, how much, find, calculate, which...," which can lead us to the purpose of a problem. Once students figure out the goal of a problem, comprehension (assuming they know the words) often comes quickly. Of course, if a student doesn't know vocabulary or syntactic structures in a problem, it is necessary to explain them.

Asking the student what makes something confusing is an essential part of tutoring! Though students don't always know why they're confused, their self-knowledge is always a great resource. Having these conversations also promotes independent learning because they encourage students to use their own awareness of what is difficult for them to develop a strategy for a problem. Often just articulating what makes a problem difficult is enough to chart a path to a solution.

Praising students is really important! Students who are struggling in a subject always have skills in that subject - just not the skills they're expected to have. Praising students for what they can do can build a foundation of emotional safety, allowing students to take risks (guessing answers, sharing half-formed reasoning) that they wouldn't otherwise share, allowing for mathematical conversation that promotes learning. The goal is to avoid the phrase "I am bad at...". That phrase does not support learning, and I never believe that about my students.

Asking questions, both while a student solves a problem and after. With some students, I assign homework. I often ask students to plan a lesson around the topics we've covered - this assignment gives me a window into what parts of the material students have retained, and which parts have fallen away.

Understanding can't be evaluated simply by checking whether a student gets a problem right or wrong - I can only see if students understand ideas by talking to them.

Begin with praise! Students do a lot of things right that get overlooked. Tell them what they're good at, and cast doubt on statements like "I am bad at math". Confidence is also built by increasing the challenge-level of problems that students receive once they experience success. Let students encounter challenges, and remind them that struggling with a problem does not mean they're bad at the subject or bad in any way. It means that the problem they're working on is hard!

I evaluate student needs through conversation with the parent and the student and through observation of student work during tutoring sessions. All three are important sources of information and give pieces of a complicated picture of the student's mathematical knowledge so far.