I recently took a GRE exam as part of my application for a PhD program in Mathematics Education. The exam consisted of several sections, all timed at either 30 or 35 minutes. There were essays, verbal reasoning sections and quantitative reasoning sections. It has been since my undergrad that I’ve written a test and man did my test anxiety rear its ugly head! The only way to prepare for this test was to practice each of the sections, over and over again. Ironically to me, I was struggling to finish the quantitative measures on time. I knew how to do all the math involved but that 35 minute timeline never seemed quite enough. I had immediate sympathy for our students. Many students struggle with math anxiety and often never perform as well on unit tests as they do during classes, yet, many teachers still use tests as their only form of assessments and give students grades based solely on test scores. This experience made me re-think assessments and what I experienced was that I didn’t necessarily show my best work during a test. I can do so much more when I’m not trying to perform on a test. Is the same true for our students? I believe it is.
The reason I am sharing this story with you is because I think we, as educators, forget what it’s like to be tested and, more importantly, how inaccurately many tests are in showing what we actually do and don’t know. I could solve every single math problem that I tried….but not necessarily in the 35 minutes that was allotted to me. If I had not finished them all, my score would show that I only have some knowledge of the mathematics, which is inaccurate. I strongly believe (and have well before this recent experience) that timed tests should be no longer! I love that the teachers at the school I currently work at don’t time tests. Students can take more than one period to complete them, without penalty. This way they are actually showing so much more of the math that they do and do not know.
Assessments are crucial in good mathematics education. However, I am not talking about the summative quizzes and tests that we use to assess the student’s level of mastery before moving onto the next chapter/concept/topic. I am talking about assessments that actually HELP our students to grow and improve their mastery. I am talking about assessments that HELP you, their teacher, to plan your lessons based on your students’ needs and current levels of mastery (rather than ‘getting through the curriculum’). These assessments are 100% necessary for a successful program. So, how do they differ from those summative tests I referred to earlier? Here’s a quick summary:
Diagnostic assessments can be used at the beginning of a school year to ‘screen’ students. This wide-spanned assessments give a snapshot of which students might be in need of intervention (if they are performing well below grade level) or a challenge (they have full mastery). Recently, I have been using more pre-assessments, which are also diagnostic assessments for each unit of study. This way we can see clearly what the students already know and where the gaps are. It helps us, as educators, plan more effectively and also allow for more personalized and differentiated learning. It also helps the student to see where his/her strengths are and what goals for learning they can set for themselves. These are not to be used for grades, but are there to give information – both for the students and teachers.
Formative assessments are done throughout a lesson and/or at the end of each lesson. Formative assessments can be: reflections, ratings, ticket out the door, using individual whiteboard paddles. Using manipulatives is a great way to do formative assessment, because the learning is quite literally visible. You can assess by watching them whether they understand the concept or not. Formative assessments are also not used for marks. They are used for the teacher to see what they need to plan for tomorrow’s lesson. Perhaps some students totally ‘get it’ and are ready for a more challenging application problem, while others may need some more guided instruction. Formative assessments help us to differentiate and ensure that all students are being challenged but also receiving intervention when needed. Using plenty of formative assessments helps to prevent poor grades on summative assessments.
Rubrics are used extensively in other subject areas but rarely in mathematics. They are a wonderful assessment tool because they give students very specific feedback about where they are showing mastery and where they need to improve. I have enclosed a picture of a math quiz rubric that a colleague of mine is using. The students are then asked to set a learning goal so that they can achieve and demonstrate mastery. What do you think gives better feedback a score of 7/10 or what you see below?
Self-assessing on rubrics is also valuable- both for the teacher and the students. I often have my students fill out the rubric first and then I go over and see what I agree/disagree with. If a student scores themselves quite high but on a summative assessment, they have not demonstrated this, you can start a conversation with them about the discrepancy. Usually either the student realizes that they’ve over-inflated their mastery or they do have a good understanding but didn’t demonstrate it on that test, but can demonstrate it to you during the interview. I have only begun to research the effects of self-assessments but from what I’ve read so far, they are meant to be the most effective of all feedback!
Assessments need to be useful for students as well as teachers. They are not there to just give us the grade for the report card but rather are important tools for giving very valuable feedback to students. Incidentally, I just read an article about the effects of giving a grade versus qualitative feedback and the findings were really clear: students who receive written feedback WITHOUT a grade, showed the greatest growth in achievement!
Educating Now was created due to teacher requests to have Nikki as their daily math coach. The site has lesson by lesson video tutorials for teachers to help them prep for their next math class and incorporate manipulatives, differentiated tasks, games and specific language into their class. Teachers who use the site can improve student engagement and understanding, in addition to saving prep time, by watching a 10 minute video tutorial and downloading a detailed lesson plan.