This April I will have worked an entire year as a tutor and adjunct instructor at UC Clermont, a community college branch of UC that happens to be in my hometown. Here are some things that I have noticed as an educator here, specifically in my role as a tutor:

- It seems more than anything,
**tutoring is about assurance**. Many students will come to me not for an explanation but for verification or affirmation.*“Am I doing this right?”**“I haven’t been in a math class in 20 years.”*(Many students are non-traditional.)*“I’m terrible at math.”*I make sure to respond to these statements with a smile and then a polite refutation that it is alright that it has been a while, but that they are not bad at math. I insist on this even when it is clear they do not believe me. I ask them questions about the problem until they have verified the solution themselves. (I do succumb to temptation from time to time and say “Yes! You got it!” because many of them never receive that congratulatory response.) - Math-phobia is alive and kicking and
**our assessment practices as mathematics educators play a big part**in the continuation of this phenomena. On several occasions I have had students tells me that they didn’t understand math when they failed a test when actually they test showed they had a competent understanding, but made basic errors which led to points off. Their 68% sent the message “You can’t do math,” rather than the message “You don’t understand these topics yet,”. It is because of my conversations with students like these that I am convinced that we need to make a careful examination of our assessment practices as educators. I perform no formal assessments as a tutor, but I am constantly assessing a student in a tutoring session. I am looking for answers to questions such as

“How does the student view their abilities?”

“What does the student understand about the problem?”

“What misconceptions does the student have?”

“What is the best way to help the student create a solution?”

“Does the student understand or do they just say that they understand?”

And other similar questions. My favorite assessment question as a tutor is “Would you like to do another one?” This typically tells me if the student feels confident or not. - I have to change my mindset from teacher to tutor,
**but the difference isn’t that large**. In both cases I am following my education motto stolen from fiction writers “show, don’t tell”. It is the student who makes the conclusions and says the answer. When I teach I view myself as expositor and cross-examiner; I lead the class to discover new material and make connections by asking them questions. (Cross-examiner isn’t a perfect analogy because I ask both leading and open-ended questions.) As a tutor I am more like a polisher. I help the student hone the knowledge they have already been exposed to in their classroom–but this is also done by asking questions. Sometimes the student is struggling enough that I do have to play teacher from time to time. **Students will sometimes see a teacher as the antagonist and a tutor as an ally**. I do my best to disabuse them of this notion. Frustration borne of misunderstanding, difficult material, or grading practices mean sometimes students complain about their teacher to me. My typical response to this is to suggest to the student possible benevolent motivations of their teacher without assuming I know what the teacher had in mind. Not only do I want to avoid insulting a colleague, I want to help the student view their teacher the same way they view me as their tutor: someone working hard to help them learn.- Many of the repeat
**students I have seem to view me as more than just a tutor**–as well the tutors in other subjects. They come to us for advice or just to chat. I enjoy building this kind of relationship with students because of my background in secondary education where I saw students every day and got to know them well. While I have had success building good rapport with the students I have in my role as an adjunct, it is more difficult to do when you only see students once or twice a week. **There is less pressure as a tutor to be the source of knowledge.**Although I try to create situations in my classroom where students are the source of knowledge, I still feel the pressure to fill the role as the all-competent, all-knowing expert as the professor in the college classroom. Although I do work hard to be knowledgeable and competent in my content areas, I want the students to become those things as well. This pressure comes from my own pride and expectations of the students, but I cannot use that as an excuse since it falls on me to create a classroom where the students move away from this mindset. As a tutor it is much easier to admit ignorance for a particular problem or topic, but this turns out for the better because it creates a dynamic where the student and I learn together. “I don’t know how to solve this problem off the top of my head, let’s figure it out together.” My goal as an educator in any context is to blend the two: a competent, knowledgeable teacher who works with the students.**My pedagogical content knowledge of material traditionally taught before 7th grade is sorely lacking**. This is most glaringly apparent when I have a student who is struggling with fractions. This is a need that we often have to meet at the Learning Center because our college has open enrollment. It is the students who struggle with adding real numbers, dividing fractions, or knowing order of operations that are the most challenging to work with. Although I can explain the algorithm or come up with any number of analogies to help, it bothers me that I am sometimes unable to provide a model that will give the student true insight into what is going on when they multiply or divide fractions. Currently I am investigating using LEGOs as a manipulative. This may be the biggest need that our center meets and where I feel the weakest.

Now, take the image of the educator I am that you have formed in your mind and discard it. These points are the ideal me, what I strive for. Sometimes when I feel pressured or busy I do not always make the student reach the answer themselves, but give it to them instead. Most days I love talking to my regulars and other days I would like for them to leave just a little bit sooner than they do. My answers to questions are not always as clear or as thorough as they should be. I am content to say “flip and multiply” when the student doesn’t follow my carefully explained exposition of a multiplicative inverse. I have to rebuke the misguided feelings of superiority I have inside when I tell a student, “Now, your teacher said do it this way and you need to do it the way they want, but the way *I *like to do it is…” and if I explain index and summation notation to one more statistics student, I may die.

The past nine months I have spent as a tutor have been very valuable to me as an educator because it has given me the time and the space to sharpen how I interact one-on-one with students, an opportunity that is not as available in amount or intensity teaching in a classroom with upwards of 30 students. The content from high school that slowly leaked out as I worked through the content of an undergrad in mathematics has been refreshed in my mind. This job also provided the platform for me to land a job as an adjunct instructor and continue to improve as a classroom teacher. I feel very confident in my role as a tutor, but I know that I have a lot of room to grow as a teacher and educator in general.

You’ve done a great job summing up what I learned from my three years as a tutor. Tutoring is so rewarding, and I definitely think it affects how you teach (in a good way).

Thanks!

Having been a tutor and a teacher, and now an instructor for undergrads, I couldn’t agree more with this whole post.

Something you might find useful for fractions: the Rational Number Project has wonderful activities and a template for fraction circles that you can make (or your students can make and keep). I have used them with both adults and children to build understanding of fractions with great success. And they’re free! My advisors are 2 of the curriculum developers, which is how I know about it, but I really wish I’d known about it sooner! Here’s a link to the first curriculum (you can get to the other on the website): http://www.cehd.umn.edu/ci/rationalnumberproject/rnp1-09.html

Wonderful! Thank you for the encouraging words and the resource!