It seems that a common, underlying theme I have found in most of my education classes is creativity. It is never really stated – we don’t have an “Intro to Creativity Class” or an assignment requiring us to showcase our creative soul or anything. But I have found that it is essential, if you want to do well as a teacher and as a student learning to be a teacher, to be creative. Forming lessons that encapsulate an outcome or big idea in a way that promotes student understanding, creating math questions that challenge students but also breed inquiry, adding Treaty Education into every subject in a wholesome way that does not damage the integrity of the subject. And creativity, have I ever found that creativity is essential in working with assessment.
There are two types of assessment that I really want to focus on. Particularly because I feel like they are not always done well in classrooms, and I really do think that they are important, because I think that knowing how to guide your teaching is such a simple way to show students that you care about them, know what they are struggling with, what they excel at, and are tailoring your unit and lessons to them and their abilities. The two I want to focus on are diagnostic assessment and peer/student assessment.
In my EMath classes, we have been learning about the Five Practices and how to teach mathematics in a way that promotes student understanding first. Students are encouraged to solve an open-ended, or open-middled questions in any way they see fit. There is not one way to tackle the question and, in some cases, not one way to answer the question. The questions have many access points so most students can even simply get a start on the question. An example of a lesson I have written using the Five Practices can be found on my blog. Anyway, one of the first parts of creating the lesson is anticipation, coming up with multiple methods that could be used by students to tackle the question and what barriers/questions may be encountered when using the method.
Anticipation is always the most difficult part of doing the Five Practices for me, because it’s hard to think in more than one way. But this is where diagnostic assessment really comes into play. Once you know your learners, and you know them well, you will learn what kind of minds they have, how they think and what parts of their math skills are stronger than others. And once you know all that, you can start anticipating with more and more accuracy. And getting to know your learners can be accomplished through diagnostic assessment.
Diagnostic assessment is a way to pre-assess students, show what they know and where their strengths lie. In ECS 410, we can up with a list of many different ways to pre-assess students, and the ones that I was the most intrigued by to try in a math class were the KWL charts, a cardstorm activity, and a modified version of a quiz, or test.
KWL, or Know, Want to Know, and Learned charts are interesting to me for the same reason that the cardstorm activity is. One thing that we seem to let slip when we teach a subject, any subject really, is the understanding part. We often think it’s enough that a student can do well on a test, tell us what 2*2 is, write out the year the war of 1812 took place in, write a poem that includes synesthesia, or draw a hydrogen atom. But the question ends up being did they just rote memorize what they thought would be asked of them, or did they really understand what they were learning? Can they tell me what it means to multiply numbers? Can they tell me why poets use synesthesia in poems? Can they tell me why the hydrogen atom is drawn as it is? And that is where I really find an activity such as the chart or the cardstorm are useful.
They make students put into words, or descriptions, what the math really is and what it means to them. It shows their thinking of a certain concept. When you do KWL chart, it shows what the students want to learn, so it gives you a place to start in your teaching. It gives you what interests students have in that particular concept.
When you do a cardstorm, you allow students to group together all of their words, symbols, pictures, and phrases and give each grouping a title. Having students explain their thinking in the groupings as well as which sections are their favourites and least favourites help you as a teacher to see which areas of a concept are their interests, or what they understand, as well as which areas they may be struggling or disinterested in.
Both activities are also useful in that if a student cannot articulate or explain any pieces of the concept that delve into the meaning of the subject, then they do know have that understanding, and must then be taught it.
The first two really give a clear picture of students’ interests, disinterests and understandings, but the quizzes are where student thinking is apparent.
Using a quiz with multiple open ended questions that all relate back to the core concept being taught are really what I think tests are for. Tests shouldn’t necessarily be marked – that way a student is not afraid to write whatever they are thinking or however they are solving a question, and they are also not afraid of getting the answer wrong. The quiz is also useful to the teacher, because it shows them they ways in which students instinctually answer a question. Adaptations should be made for students if they need it, because it will help accurately show exactly how that student learns. I, for example, would have much preferred to be able to talk during tests. It didn’t need to be to someone, I just need to voice my thoughts aloud to hear if what I’m thinking makes sense, and logic out the question. If a student needs that adaptation, it is helpful to know that ahead of time before it becomes a problem later.
When I was in class, the only time we were given toward student or peer assessment was either when we were self-correcting tests, or when the teacher paired up students who were struggling with those who were more advanced and got them to help struggling students. While I do think that both are useful methods of student/peer assessment, the way in which we did them didn’t do much help. The marking was done with the teacher giving us detailed instruction on how to mark the tests and there wasn’t really any room for students to use that assessment to better themselves, we had already done the test, and so we were simply evaluating our mistakes, with no chance for improvement. The second was done with the teacher literally outlining that the “smart kids” would be helping the “not-so-smart kids”. Which is a horrible thing to say, because I don’t necessarily believe that a student can just be labelled, or written off, before you learn exactly why it is they are struggling.
In Making Classroom Assessment Work, there is a section on self-assessment that demonstrates why exactly it works using a line with loops in it. It shows that, when a teacher assesses regularly, there are many loops. But, if a student and their peers also assess the work of a student, the number of loops can double or triple. And while a teacher can only assess once in a period of time, the teacher can have students self and peer assess before they hand in assignments to be assessed by the teacher in order to have the students get two more chances to make sure that the work is meeting all of the expectations of the assignment. And what is also noted is that the students and the teacher came up with the expectations together.
I think that giving students the chance to do that last chance assessment is really useful, because there are a lot of little mistakes that we cannot see ourselves in our work that a fresh pair of eyes could easily identify. Maybe we copied a question down wrong, maybe we forgot that our teacher prefers we don’t use contractions in formal writing. But also, before we give it to that peer to look for those mistakes, we ourselves also get a chance to make sure that we are comfortable with having others assess it. Sometimes, having that pressure of immediacy, of having the assessment be directly after we hand it to the peer will be just the incentive needed to look over that paper, that assignment, that picture we drew one more time to make sure we are proud of it, or accept that it is our work.
I know that when I do work, I often feel so burned out by just finishing it, that I can’t imagine reading it all as well. And, like most, procrastination is my friend that tells me I can just put an assignment off until the last possible moment, and it’ll be all fine. Giving students that time to look it over, to have it emphasized to them that they should look specifically at how their work matches up with the rubric before passing it to a peer to do the same gives them that time, that opportunity to do the work they didn’t find time for at home.
The final point I want to address about self-assessment is the metacognitive part of self-assessment. Self-assessment makes students think about their thinking. In the text, it mentions that students who have no extra support in the classroom may really benefit from using metacognition, because it helps them to reflecting on how they learn, which they can then articulate to the teacher, so that the teacher can teach them better.
As I mentioned before with the Five Practices, knowing the way your students think is extremely useful in the classroom. And getting students to help you identify what type of learner they are, and how they go about solving problems can help a teacher help their students all that much more. Like with the loops, a teacher can only get so much done in the time they have, so having students do some of the work themselves can save a lot of time, and also be beneficial to the students.
The biggest thing I would have students do to self-assess in math would be to have them outline why they answered questions the way in which they did, or why they decided to use that particular approach. Like I mentioned, I think it is essential to have students understand what it is they are learning, as well as why they are learning it, and as the target in the assessment text shows, when students monitor themselves, know the language of assessment, and are invested in learning, they can be lead to understanding all that much more. Having students articulate why they multiplied two numbers together shows that they understand what it is that multiplication does to numbers and how it is necessary in a question. On the flipside, it may also show them that it doesn’t make any logical sense for them to have added two numbers, and so, they need to look at how they solved a problem again to maybe edit it.
The importance of assessment is shown in the growth that students can have the opportunity to make when the direction of the learning is geared toward their previous understanding, and also in the way that students get a chance to think about and understand their thinking and the thinking of their peers. If students are involved in their assessment, they are involved in their learning, and it makes the lesson we agonize over stick, and it makes the learning feel important and involved to the student, so that they have responsibility and autonomy over some of their learning process. So, how will I involve all of this assessment in my classroom? Well, to tell you the truth, I have many ideas, like some of the ones I outlined above, but I am still growing, and still learning. So I will just have to learn more, get creative with I learn, and change my math classroom, or any classroom I have into one that has more than just tests and quizzes.