Assessment Article Review ~ Using Learning Logs in Mathematics: Writing to Learn

This article was written to inform educators of the benefits of using learning logs/journals in the classroom. The author of the article stated that Learning logs function to assist students to reflect on what they are learning and learn while they are reflecting on what they are learning. As students use learning logs, they are actually keeping a running account of their understanding and thought processes in regards to math. This shouldn't be focused on grammar, but rather the content to ensure that the student is becoming proficient in their learning. This is also a great way for educators to track what the student is learning, what areas in which they need extra help, and to see how the lesson went from that day.

Some teachers mentioned their reasons for not using learning logs were class time and teacher time. They expressed the issue of it taking so much time out of the day that they would rather use an assessment method that is more direct and that takes less time. The article mentions that the students could be given a time limit of 10-15 minutes depending on how long the students need, and it would take about 5 minutes per journal to read through and make comments. It is very important that teachers make comments that are full of positive reinforcement because it helps the students to attain a positive disposition towards math. This positive feedback from the educator also empowers the student and makes them want to strive for further excellence.

Reflection:
I think that this could be a great way to track how the students are processing the content being learned. It is also a great way to keep them engaged in mathematical reasoning and communication which is key to understanding math. I was thinking that it would be neat to incorporate technology by having the students develop an online blog for their journals. I don't think that this should be the only assessment technique used as it is not a complete and thorough type of assessment. It should rather be used in conjunction with another type to ensure both quality and quantity in assessment.

McIntosh, M., Draper, R. (2001). Using Learning Logs in Mathematics: Writing to Learn. Mathematics Teacher 94(7), 554-555

Journal Article Review: Identifying Logical Necessity

This article explains the increasing importance of teachers being able to make sound judgments in regards to the logic that is often used in mathematical arguments. Logical Necessity is defined as the condition for which conclusions follow necessarily from premises. Throughout the article, examples of student work is given. These examples include problems from which individual's have to determine the correct solution based on the correct logic. They are to give their own logic and then they also look at students' logic to determine the correct response.

It is shown that through feedback from the instructor concerning specific ways the student can improve, the individual will improve and correct logic will start to become more natural. It is vital that the instructor not only show the student where they are wrong, but must give them direction in how to improve through proof and reasoning. Logical Necessity should not only be taught in the elementary school, but in other subjects as well in order to more thoroughly equip themas they progress through other grades.

According to Stylianides's conception of proof, it is a mathematical argument, a connected sequence of assertions for or against a mathematical claim that follows: statements, argumentation, and representation.

It is proven that teachers who exercise logical necessity in their reasoning and proof will also be able to instill this skill in their students. It is important to teach learners how to reason answers through logic and proof; not just what the answers are.

Journal Article Review: The Value of Guess and Check

This was an interesting article that talked about the Guess and Check method. This method has proved to be advantageous for students in the middle grades; especially as they work through word problems. Many times, students give up and get frustrated when it comes to word problems because they don't actually understand what is being said because they don't have a working knowledge of mathematical language. These students end up following a set of guidelines and formulas instead of comprehending mathematical application and critical thinking.

This article suggests that students use guess and check which will enable the student to develop a conceptual strategy to make sense of word problems and to find the appropriate solution, pattern, or equation. Students start out with a series of questions that guide them through the process. Through this process, students develop a strategy and skill that is useful to them in all facets of life. This allows learners to go from an objective view of mathematics to more of a subjective approach as they delve into symbolic representation. Learners must not only know how to use this approach, but know when it is the most useful tool and when it is not.

Guess and Check is an incredible tool for students to grasp because it brings a direct correlation between understanding concepts and symbolic representation of their knowledge. It is also a way of not only finding solutions to problems, but rather getting into the habit of exercising critical thinking within math to create mathematical equations.

Video Blog #2

Lesson Analysis 1: Identify several strategies the teacher used to orchestrate and promote student discourse in this lesson.


The teacher would get down on the students’ level and ask them guiding questions that made them think critically through their own problems. This got them thinking together to come up with their answer. It also helped them talk through how they were getting their answers through justification. The teacher also gave other examples while talking with the students that helped them to make deeper mathematical connections within their groups to fully understand their own math problems.


Lesson Analysis 1: Provide 3 examples of evidence that students have learned the mathematics being taught.

The teacher would get down on the students’ level and ask them guiding questions that made them think critically through their own problems. This got them thinking together to come up with their answer. It also helped them talk through how they were getting their answers through justification. The teacher also gave other examples while talking with the students that helped them to make deeper mathematical connections within their groups to fully understand their own math problems.
1. One of the students was able to present her group’s work with excellent articulation of not just the answer, but how the answer correlates to the graph. She student was able to make accurate connections and patterns from the graph.
2. As the teacher asked the students how they got their answer, they were able to tell the sequence they generated and also how they got the equation. They were able to justify their answers.
3. The students were actively engaging in conversation with the teacher about their mathematical reasoning. They were using critical thinking to process the mathematical equations.

Reflective Task 1: Describe the student-teacher interactions during the task debriefing discussions and assess the effectiveness of these interactions.

The teacher asks the students questions that prompt the students to clarify what they have said. The instructor allows the students to “teach” her their thought processes and when she gives them verbal clues that she understands where they are coming from, she gives them different angles to think about. I think this is a very effective technique because it helps the students to think through their thought process and fine tune their strategies. It also challenges the students to think deeper and gives them more ways they could approach the problem.