Author: acorrigan

I have several reasons for being wary of giving out grades in school. The effects of grades on the reason for students to learn and the type of learning they engage in is one of the reasons and was brought up by Kohn in his article, “The Case Against Grades.” Another reason that I’m not fond of giving out grades is because the current system of grading evaluates all students on the same scale and assumes that they are all capable of achieving the same success. Marks are given out of 100% but I question whose version of 100% that is. Not all students are able to achieve to the same level so I believe it would make more sense to grade students on how well they are learning compared to their individual potential. Of course, this opens a whole different can of worms about how to determine what a student’s potential is and the dangers of saying that some students have less potential than others.

I believe that the suggestion that Kohn gives is a solution to these issues. Rather than giving grades, give students qualitative feedback. I think this could be great for all subject areas. In many of the classes I have been in, which tend to be math classes, I have often heard the teachers talk about how students should reflect on their grades to determine their level of understanding. While grades may be an indication that students need to continue working on developing their understanding of the concepts, they are typically not very good at telling students exactly what it is they need to focus on. I think that giving qualitative feedback can help give students explicit feedback on specific areas they need to work on which has the potential to be more effective than having students attempt to interpret what their number or letter grade is trying to tell them. I think it is an interesting idea and would love to see if anyone has done research to test the effectiveness of this type of evaluation at the high school level.

I think it is really important for math teachers to include performance based methods of assessment in their math class in order to show students a different side of math than what I think many people are used to. Using these types of assessment techniques are often great for showing students how math can relate to the real world and also allows them to have some fun when using math.

While on my short practicum, I did an activity with my Math 8 class where they were given a menu from a restaurant that I had created and were asked to choose one appetizer, one entree, and one dessert and then calculate the tax and tip on the items as a part of their assessment for the calculating percents unit. My SA does a similar activity with his classes where he brings in Best Buy flyers and the students are given a certain amount of money to spend but they must add PST and GST into their calculations. Given more time, I think that a project like this could be further expanded to have the students have to calculate what a restaurant should charge for each dish if they were given the cost of the ingredients and told that they should make a certain percent profit for each dish.

Activities like these are often fun and help students remember the concepts and procedures a lot better by helping to cement them in their minds. However, I think that it is important to recognize that certain types of questions on a typically formatted math test can also help to evaluate students’ understandings of concepts at a deeper level. When many people think of math, and the textbook alludes to this as well, they think of the rigid, black or white, one answer only type of question that have frequented math tests and texts. I believe that it is important for teachers to include open ended questions that require students to think at a deeper level and show a complex understanding of concepts in their assessments in order to properly assess learning. This is an idea that I think is becoming very popular in math classes nowadays and I think can help evaluate students in the same way as the performance based assessments because they require a very similar form of thinking.

As a teacher, I am to use plenty of performance based assessments and open ended questioning to try to help my students to the greatest of my ability.

I really liked the idea of the partner problem solving for math. I think it is a good way to expose students to different methods of approaching the same question. It also gives students someone to help them interpret the content of a math problem which, at times, can be very difficult, even for high performing students. Given the proper pairings, I also think this activity can be used to get higher achieving, more fluent students to peer mentor students who may be struggling. The mentor can take the position of the listener and help clarify anything that is confusing the solver. Depending on the student, the listener may also be able to model the use of academic language. Afterwards, when the solver explains their solution, they are given an opportunity to use the new language they have learned and also explain how they extracted specific information from the written question.

For many areas in math, being able to read the material is a challenge of its own, especially when the questions are written in math symbols rather than in words. There are many symbols that are very similar in appearance and can be very confusing. Here are a few examples of these similar symbols:

There are times when students understand all of the material and know how to apply what they have learned but are just not able to because they do not understand the symbols or words that are used in the question that is being posed to them. The more students read these symbols and hear them translated, the easier it will be for them to be able to distinguish them and be able to accurately interpret them in the future. As students proceed to higher levels of math this skill becomes increasingly important and therefore needs to be developed as early as possible.

I think that Zwiers’ academic collaborative skills are extremely important n math because they are very similar to skills that students need to have to effectively do individual work. Working in groups where students are able to develop these types of skills will also help them develop their individual skills and make them better equipped to succeed in math class. Given the right pairings/groupings, students who are better at these skills will be able to model them for other students who need extra work.

Over the last month of so in this program, I have become a big fan of using group activities to get students to explore and discover mathematical relations on their own. The approach seems very effective to me for many reasons. First, I think it increases the likelihood that students will be able to remember the material. As a student, I always remembered the concepts that I discovered on my own more than concepts that were dictated to me in a way that made them something for me to memorize or forget. Second, I think it allows students to use and develop their academic collaboration skills. Similar to the idea of using language to authentically do and think from chapter 3, these are skills that need to be developed, honed, and used on a regular basis. In terms of these skills, I think the idea of ‘use it or lose it’ is very relevant. Lastly, I think that these types of group situations can be very helpful in exploring the relationships between different mathematical concepts and finding and understanding multiple ways of approaching the same problem. Students are able to come to a shared understanding in some situation, as Zwiers suggests, but in math they are often able to do this in a variety of ways. Working together can give students an opportunity to see different approaches to problems which can help develop their understanding and, ultimately, make them more well-rounded math students.

Some of the group/pair techniques are difficult to use effectively in a math classroom but I was drawn to the idea of using a jigsaw type of technique. Once again drawing on the idea of having students solve the same question using different methods, I think an activity where students are given the same question and then break off into groups to solve it could be very effective. Different groups could solve the question and then present their methods to the classroom. Some groups may have come up with ways of solving the problem(s) that other groups did not think of. This could be really effective as an end of the year review activity.

I think that asking open ended questions in a math class can be particularly important and beneficial. Often it is the case that students can come to the correct answers without having any real understanding of the material. Open ended questions can be used to more accurately evaluate whether students are really comprehending the material whereas ‘display’ questions have the possibility of hiding misunderstandings. Additionally, I think that they provide examples that are similar to think-alouds. With the open ended questions, students are able to hear how their peers think and reason their way through problems in addition to the way they are hopefully already hearing their teacher think and reason. They provide opportunities for teachers to correct erroneous understandings that many students may have which helps the teacher address the entire class at once rather than waiting for an assessment where students have made mistakes to realize their mistakes.

Zwiers also talks about the need to avoid creating an atmosphere where students look to the teachers as the validator and corrector of responses. This is something that commonly happens in a math class, I think partially because students tend to lack self-esteem when it comes to math. In other classes I have read articles where authors talk about the tendency of students to look to teachers, textbooks, or other forms of  ‘authority’ to validate their answers rather than thinking critically and validating their answers themselves. I think if students can be taught to participate in thoughtful classroom discussions they will also be better equipped to thoughtfully analyze  and evaluate their own written responses which will have the effect of making them a better math student.

I was always aware that vocabulary is important to develop a student’s reading comprehension but I was not aware of the extent to which the two are related. Reading how vocabulary can help provide students a “bridge between the word-level processes of  phonics and the cognitive processes of comprehension” makes it even more apparent how important it is for educators to make sure they us academic language in their classrooms. This would be especially helpful for ELL students.

The above is very applicable to math teachers as well. The article mentions that the majority of word learning is done through incidental learning where students are either read to or are reading books on their own. I think that math vocabulary would be more difficult to learn this way than the vocabulary from many other disciplines and I say this for several reasons. First of all, I believe that there are going to be less instances where math jargon appears in the types of books students are more likely to be reading or have read to them. Because of this, they are less likely to be exposed to the academic words related to the discipline which means students will have less opportunity to learn these words via incidental learning. The second reason I feel this way is because a large proportion of mathematical terms have more than one meaning (are multidimensional) in English which can cause confusion for students and negatively affect their reading comprehension. Many of the words with multiple meanings are ones that students are likely to encounter before they reach the level of math where they are required to apply them in their mathematical context. The article uses the example of the word ‘volume’. Chances are high that students will understand ‘volume’ in its musical context before they encounter the word in a mathematical setting. Math vocabulary includes many other words that have multiple meanings (function, series, factor, mean, mode, median, power, expression, root, etc) which have the possibility of to make applying these words in their mathematical context harder for some students, particularly ELLs.

Because of the challenges listed above, I think it is especially important for math teachers to make sure they spend enough time working on academic language in the classroom for students to establish a proficient vocabulary. I think direct instruction is a good means of achieving this but even more, I like the idea of a think aloud. As mentioned in the article, a variety of methods is the best way for students to improve their vocabulary and, in turn, their reading comprehension however I like the idea of a think aloud because it helps with vocabulary as well as with showing students tips for how to approach a math question. In the end, regardless of how it is done, intentional word learning is going to play an important role in developing the vocabulary of a math student.

I believe that Fang and Schleppegrell really hit the nail on the head (pardon the figurative language) when they urge educators to make discipline specific ways of using language explicit to their students in order to help them better engage with the knowledge presented to them at school and to help them develop literacies across academic content areas. I know I have experienced many moments during my undergraduate degree where the readings were saturated with academic language that was completely foreign to me and the sentences were so complicated I often had to read through them multiple times just to attempt a guess at their meanings. There is nothing like an unfriendly, structurally complicated sentence laced with jargon to make an individual’s eyes glaze over and turn them off of a subject.

In order to minimize these types of negative outcomes from getting students to interact with academic language, they need to be taught a way to successfully wade through all of the academia. I am very attracted to the functional language analysis discussed in the article because it appears to give students the tools they need to apply the approach on their own to multiple disciplines.

Because of the practicality of this approach across subjects, I would argue that developing these skills in students should not be the responsibility of teachers in any particular discipline but rather a team effort where all teachers do their best to show students how to make sense of the complex academic language that they will increasingly be presented with. Further to that, I do not believe that these are skills that students need to wait to reach secondary school to begin developing. It makes sense, to me, that students would begin to be familiarized with functional language analysis, or some other method, before the point in their education that they will have such a strong need for them. Perhaps middle school would be a more effective time to introduce students to these ideas so that they can have a strong enough foundation to easily adapt to the new rigors of high school. However, that is not to say that secondary school teachers should then have no responsibility for the development and solidification of these forms of analysis. When I say that the development of these tools should be a team effort, I mean that it should be so throughout the entirety of a students educational career in order to best serve the needs of the students.

Before reading the first few chapters in the text, I had never given much consideration to the difficulty of learning new academic languages for students who have not fully mastered the English language. I was born and raised in Canada and grew up in an English speaking home which meant that I never had to experience the struggles of learning multiple languages at the same time. Reflecting on the language used in math (my area of specialization) I can see how this could become especially tricky for some students. Words such as “prime”, “difference”, or “product” have a completely different meaning in the context of math than they may have in a persons’ every day life. After being made aware of the many possible traps waiting to confuse students I was surprised to see some of the solutions that were listed in the book. Suggestions to overcoming these obstacles such as using facial expressions, hand gestures, and metaphors seemed so obvious and yet I had never thought of them as tools that a teacher could consciously take advantage of to aid in the education of their students. Previously, I had thought of these things as a natural part of conversation that was given very little thought. This made me realize that there are some seemingly small things that teachers are able to make a conscious effort to do that can make a world of difference for students.