Asking for Help – Advisory board, Advisors, and Peers

You will not survive grad school if you don’t learn to ask for help.

My advisor told me in my first year that I had to learn to start asking for help or I wouldn’t survive the program. Asking for help was a challenge for me: I don’t always notice when I need help. I’m scared to admit vulnerability. I’m not sure whether it’s a good question or not. I’m not sure if the person I ask will use it against me or actually give me good advice.

Ask for advice early and often.

For big things (e.g., research projects) and small (e.g., this conference is overwhelming), asking for help early – as soon as you notice you are struggling or even before you are struggling – makes it easier for people to help. The Preparing to Teach Algebra project began in August, 2011. We had our first advisory board meeting four months later in December, 2011. In their written response, our advisory board thanked us for meeting with them early enough in the project that we could use them effectively. They were able to help us find our way before we got too far off track.

Later in that school year, I co-presented with members of the Strengthening Tomorrow’s Education in Measurement project at the annual conference of National Council of Teachers of Mathematics (NCTM). I attended the research session and the regular conference, so I was there for a week. After the first day, I was overwhelmed with the sights, noises, and social interaction. I asked a colleague what I could do and she told me she had the same problem and her strategy was to sometimes put on large headphones – even if she didn’t turn on music. It indicated to the people around her that she was not to be disturbed, and she could take the time to reset. This experience of confessing my struggle, finding out it was shared, and that someone had a strategy to deal was simply amazing. It helped me learn that I can ask for help.

Team- and Community-building

Many people enjoy feeling useful and enjoy feeling smart. Asking for help isn’t only about you and showing weakness. It’s about giving other people a chance to help you, a chance to show their thinking, and a chance to see that they aren’t they one with that struggle. By asking for and receiving help, you can build bonds that create a strong team or community.

Getting smarter by sharing strategies

In K-8 mathematics methods courses, we share the value of sharing and discussing strategies in order to understand mathematics more deeply. Sharing strategies is helpful in more than mathematics, but also in life. We all have room to learn from each other and develop more sophisticated strategies of dealing with challenges.


Meeting Judit Moschkovich

Judit Moschkovich met our first-year “Introduction to the Math Ed World” course. She told us that the first step in teaching social justice has to be teaching for understanding.

What are goals of teacher education for teachers who will be teaching English Language Learners (ELL)?

More important than language proficiency is the mathematical reasoning. Even for native speakers, being articulate is hard! You may think they (and you) are saying things in a mathematical way, but they may not be. Move away from simple views of what mathematics language is: It’s not just a list of definitions or vocabulary. Vocabulary is important too, but the best way to learn vocabulary is to use the words with purpose not just “give me a sentence using the word divisor”. Learners also need to practice the complexity of language through exploratory talk (with peers) and expository talk (in presentations). We also need to teach children to read: Math textbooks and word problems are different kinds of reading that we need to teach the children to do. Remember that everyday context and objects can be used for reasoning, not obstacles.

“For some definition of …”

I think the best thing I’ve learned in prosem this semester (our “introduction to the math ed world” course) is the importance of definitions.

Definitions in Mathematics

In math, definitions are important. Definitions can build on axioms or other definitions, but basic defined terms rely on “primitives” that are assumptions about the “basic facts.”

Note: In order to be perfectly precise, we would need to define everything. But definitions rely on words.  One word cannot be defined without relying on other words.  For those other words to be defined, more words need to be used. This is why we use primitive terms even though they are not at all precise. This means we have to be very careful about assumptions we make regarding primitive terms – sometimes we will assign properties to the primitives but unless that happens we can’t assume properties.

It’s how mathematicians set the stage to do math. In mathematics, being precise is everything. Some choices when creating definitions are based on conventions and others are based on strategy. A mathematician could arbitrarily assign any meaning to a symbol or term, but they need to communicate to others so paying attention to conventional use is important. (Although some of the most interesting mathematics results from mathematicians choosing to ignore certain assumptions or to change elements of definitions.) Mathematicians also make strategic choices to make later theorems weaker or stronger and (often) easier or harder, respectively, to prove. So, definitions are important in mathematics to communicate and to set up later arguments.

Definitions in Mathematics Education

Choices about definitions of terms in Mathematics Education are similar to those in Mathematics. Still, a math ed researcher needs to make decisions based on convention and strategy, to communicate and support arguments. A difference is that it is more difficult to be precise in language, when that language has to describe the complexities of life, teaching, and human beings. It is still important to reflect on definitions and attempt to be precise, however. It is difficult to look at prior research that has “taken-as-shared” meanings of terms or processes.

For example, in my reading, I see many studies that attempt to measure the effects of technology in teaching. As one example, many studies measure the effects of “use of graphing calculators to support student learning of functions.” But those studies do not always describe how the graphing calculators were used: Did students use them only to calculate values or graph functions? Did students use graphing calculators to explore the parameters of functions, making and testing conjectures? Did students gather data with calculator-based rangers (CBRs) and the explain the effect of changes in the movement on the function? These are important differences.

Arguing without Defining

I have often found myself in heated “discussions” (and by “discussion,” I mean “argument”) that ultimately end when we realize we’re both fighting for the same idea, but using words in different ways. Taking the time to define terms is important in research and in real life!

Communication is so difficult in everyday life because we all come from different communities (even communities of one) where different norms are accepted as the only norms and where meanings remain unexamined. But, by examining our meanings, we can be more aware of others’ different meanings. This awareness can make communication easier and more satisfying, and can open up potential communities. (Well, I think so.)

Notice that I did not define terms in this blog post. Oops.