Unit 4: Utilizing Math Journals for Student Success
Welcome to Unit 4!
Welcome to the last, but not final word on mathematical literacy and mathematics journals. This section is meant to highlight on the personal qualities of usage for mathematics journals. Not every classroom, learner, or teacher is the same. Therefore, something so highly personal as a mathematics journal should no look standard across every grade, every classroom, or every year. Keeping this in mind, I hope that you enjoy these beginning, foundational thoughts about the usage of mathematics journals. And I hope that you will choose to further your own knowledge of the dynamic uses of mathematics journals.
Using Math Journals
Incorporating a mathematics journal into the classroom can be a great tool not only for students, but also for teachers. Sometimes in mathematics, a very expansive and complex subject matter, presents opportunities where students need to reflect on their exploration to make sense of everything. Students are able to handle the more complex topics of mathematics when they are given opportunities to reflect, evaluate/analyze, express, and record their problem solving and mathematical reasoning. On the opposite side of the coin, teachers are given a unique opportunity to evaluate progress based on the way that students chose to present their learning. They can help students learn to make connections over time and develop strengths in mathematics, while also evaluating progress in key understandings across units of mathematics. When used appropriately and authentically, the mathematics journal becomes a key classroom tool.
One of the greatest features of mathematics journals are that they are flexible to adapt to any teacher's needs and preferences. The teacher helps to guide the performance and amount of time used while the students stay in control over what is presented, how, and why. Journals can be used as much or as little as needed, as long as they are used to inform instruction and learning in an authentic manner. If children are better suited to use the journals during the entire mathematics period, tracking examples and lessons while also working through example problems, then the teacher may choose to utilize a daily journal. However, if the teacher woud rather have students write end of the day entries to simply describe their feelings and experiences, the journal will take on an entirely different presentation. The one characteristic that should hold true through all types of journals in mathematics is the children must be the authority on the journal. Whether the teacher motivates the students with prompts or problems, open ended questions or even questions to further thinking, students must have the responsibility for determining the presentation of their response and reflection.
Responding To Learners
The main purpose for responding to a learner in their math journal is to learn more about what the student knows, feels, understands, or is doing. However so, not all entries need to be commented on or responded to. Teachers should be sure to read all journals and to respond weekly with sufficient detail and thought. Responding to everything in a detailed and long entry can be overwhelming and sometimes unnecessary. However, summing up learnings and connections made during the week can help students learn to do this themselves as they write in their own journals. Additionally, having summative statements and entries can help a teacher track progress across weeks, units, months, etc.
The next important characteristic of responses to learners is the quality of response given. When a teacher provides simple, uninformative comments such as "Nice work!" or "Great job thinking through the problem," they are not providing quality feedback to the student. Students will not pay attention to this feedback which is not authentically written. Instead, teachers should try to address any great points or feelings within the journal. Understanding why the journal was written or what it was based on can help to reveal areas that need responses. Another method of doing this is to offer opportunities to push student thinking by presenting them with new ideas or questions. If writing back to the journal is not the most appropriate way of addressing the feelings or thoughts, another method is to record quotes from entries as they are read, to then hold a mini-conference with the student later. As time and usage of journals increases, each teacher is able to develop their own personal way of dealing with mathematics journalling. The main goal is to ensure honesty, authenticity, and respect in responding to a student's feelings, thoughts, learning, and processes.
Criteria for Assessing Math Journals
To understand the assessment of mathematics journals, one must first understand that grading and assessment are not the same. According to Clarke, grading is a method of encoding assessment information. However, no matter what, when a grade is assigned to anything there are some things that are loss, including assessment information. Knowing this, the teacher can then proceed to assess mathematics journals. To do so, it is important to determine the criteria for assessment. Assessment should look at the quality overall of the journals, the presentation of learning the student chose, and the level of sophistication of the student's response or expression. This eliminates the idea of right and wrong from the evaluation criteria. Since mathematics journals are about reflection and expression, a grade or simple letter evaluation does not do justice or authentically assess the student's learning.
Here is an example of one such criteria that can be used, given by Clarke:
(Clarke, pg. 57)
Notice the two categories, 'quantity of work' and 'how well is it - [the information] - used?' Under each category are a couple questions as well as a heading for the sub-category. The first category, 'quantity of work' assess the frequency (how often the journal is used) and the volume (the amount of work done). These sub-categories are subjective and very open to teacher interpretation. This is an example of how teacher need and desired usage comes into play. The frequency and volume of entries will look very different in a class that writes every day over a class that writes once a week. Therefore, teachers should be sure to identify their need prior to assessing based on the criteria. The second sub-category, 'how well is is - [the information] - used?' identifies it's own list of questions for evaluation. The questions talk about the summaries of students, the examples used (or not used), errors and tasks identified as well as the discussions of them, signs of involvement, willingness to explore, and dialogue, or the asking of questions in an investigatory style. These characteristics of student journals help to look at reasoning and mathematical problem solving in the learning practices of students. When teacher analyze and evaluate these characteristics in a meaningful way they can better build a picture of each students particular learning and growth throughout units and even quarters.
Unit 4 Questions for Reflection
For your final reflection in this course, click on the discussion tab of THIS page. How did you feel about this course? What beliefs have you formed during the development of this mini-course? (If applicable) How do your new beliefs, feelings, and understandings relate to those of others who have explored this mini-course?
I hope that you have enjoyed this mini-course. There is so much to mathematics and the constructive, authentic instruction of today's mathematics. I hope that through this course you have learned something new, affirmed previous beliefs, or even developed a new interest in mathematical literacy and math journals. I wish you the best of luck in the future as you continue to learn about effective instructional design.
- Clarke, D. (1997). Constructive assessment in mathematics: practical steps for classroom teachers. Berkley, CA: Key Curriculum Press.