Reasoning and Proof Article - Can Teachers Be Too Open?

Can open ended questions be too open ended? This is the question that a researcher by the name of Amy Parks set out to answer. When Parks was a teacher she said she used a lot of inexplicit open ended questions. This caused only about three of her students to answer questions all of the time. Inexplicit question provide a wide range of answers, this can be intimidating to students. Students are not sure if they are correct so a lot of times they do not want to respond to a question. Parks thought that it would be more beneficial to ask open ended questions such that are more explicit. Such as "how did you find your answer to letter D?" and opposed to "what do you think about letter D" ( Teaching Children Mathematics, 2009)
Park observed a young boy named Marcus. Marcus was very shy. Whenever he was asked a question and would answer, he would second guess himself. When Marcus would provide an answer, his teacher would ask "why?". This would cause him to second guess himself and think his answer was actually wrong. However the question "why" can be very beneficial for students to be able to explain their answers. By describing "why" they got their answer, students are showing that they understand the whole process and not just the final answer.
Through this article I learned many valuable strategies for asking students questions. A good way to get students involved is to attach a students name to the question, for example "Lauren, why did you use multiplication for number two?" As a teacher we do not want students to only come up with an answer. We want them to be able to come up with the correct answer and be able to justify how and why they got that answer. For example you want to ask your students "Why did you add 45 and 54 together to get your answer?" This way students will further understand how they got their answer.
Another strategy that I learned that I know I will use in my classroom one day is to start off with some introductory yes or no questions. These questions can be asked to the whole class for them to answer together. These types of questions can essentially "warm-up" some students who may be shy and not normally answer questions.
In conclusion I learned that you need to ask questions to your students that require them to justify their answers and thinking. As a teacher you do not want to ask students questions directly out of a book. You want to promote thinking and understanding of a topic when you are asking questions to your students. These strategies and ideas will be very beneficial to my classroom.

Parks, A. N. (2009). Can teacher questions be too open? Teaching Children Mathematics 15 (7),
424-428.

Reasoning and Proof Process Standard

The process standard Reasoning and Proof is a standard that starts very young and continues to grow throughout the school years. A students reasoning expands and they grow and learn more. Reasoning is basically a way that can help students make sense of math. Most people remember proofs as in geometry. However, proofs should be involved in a student’s curriculum besides just geometry alone. Reasoning can become a habit and it must be used consistently in order to be developed and used.

Students need to see by an early age that everything in math happens for a reason. It is very beneficial when students ask questions like "why?" or "How does that happen?". By answering these questions for your students you can let them see why they are doing math and how it actually works.

It is important for students to make mathematical conjectures. This allows students to ask questions and figure out reasoning. Younger children often work best by exploring their conjectures through more concrete materials. However this works well for all students as well. It also works well when students can work together with one another and talk about their different conjectures and explanations. This helps students understand things that they may not have before. When students are younger their explanations for their conjectures will be very simple. However as a student gets older their reasoning should become more complex. By high school students should be able to explain their reasoning in written form. When students get older their reasoning's involve more mathematical terms and concepts.

Video Blog #1

The purpose of the activities in these videos were to show students how to see patterns in the letters of words. They were told to give a number scale to each of the letters in the alphabet 1-26. There were different tables of students and each table was in sort of a competition to get the highest number of points for all of their names. In order to do this efficiently the students had to notice which letters in their names appeared more frequently than other. For example, if all of the people at the table had an A in their name, than they would put A at a higher number on the scale. The students seemed to really enjoy this game and really get involved. A couple of times the student did get confused but the teacher would always

Discourse - Questioning
Reflective Task 2: Propose one or two summary questions that could have been used at the end of the lesson to make the mathematics clearer and more explicit to the students.
1) Why were some of your words worth more even though they were very short?
2) How can you go about choosing point values for words to be worth a lot of points, or less points?

Student Learning- Assessing
Lesson Analysis 1: Describe, with examples, how the teacher determined if students understood the tasks that were assigned.
1) She asked a group what their problem was that they had.
2) She also used examples to describe how in a team sometimes you may have to go down, in order for your team to raise up. She followed that from an example that a student had said.
3) This assessment was more informal. The teacher stated that for this lesson can better know if the students understand the information by going around and listening and asking questions. I agree, throughout the videos it seems as if she was assessing the whole time. Making sure that the students understood what was going on during each activity.

Teaching Decisions- Evidence
Lesson Analysis 1: Provide three examples of evidence that students have learned the mathematics being taught.
1) One of the tables of students figured out that the most common letters in their names at their table so they gave those two letters the highest value. That way their final score would be higher. They were looking for patterns.
2) Another group of students realized a pattern in their names as well. They realized that they all had A’s in their name so they gave the letter A the highest point value.
3) A table also gave themselves “0”’s for the letter B, because they noticed that no one at their table had the letter B in their names.

Overall I thought that the activities used in this video were beneficial. It allowed students to be able to start to think about patterns and also to think strategically. I also enjoyed how throughout the videos the teacher kept asking the students questions and keeping them engaged. She also answered many of the students questions very appropriately as well. The students really interested in the activity as well. You could sense by their comments and expression that they were really enjoying what they were doing . The students had to sit down and think about everyone's names at their tables and determine what the most frequent letters were. This seemed like a fun activity that one day I may want to try with my students.

Journal Article- Curriculum

Mathematics can be a very challenging topic to teach, especially to young children. According to the article Mathematical Concepts Come Alive in Pre-K and Kindergarten Classrooms, teachers should use literature to help students understand the concepts of mathematics. "The concrete, real-life experiences described in literature motivate students to think and reason mathematically" (Huber and Lenhoff, 226). Younger students do not realize that they will be using math in their everyday lives, and it can frustrate them as to, "why are we learning this?". In a curriculum reading literature about mathematics will help younger children see that math is part of their everyday lives and that they will be using it everyday. An example from the article that shows that literature does help students in mathematics is about two young boys who were read a book about buttons and classifying then. After the book was read they were asked to classify the buttons in groups that "are the same". They both put classified the buttons into different groups based on similarities.
Children learn by being engaged in what they are learning about. Literature helps with this as well. Through research it has been proved that mathematical literature does help students learn mathematics and the concepts. Literature should always be paired with hands on manipulatives as well in a mathematics curriculum, for example how the boys were given buttons to sort after they were read a book about buttons. As a teacher, you want to guide your students through the learning process, not just give them the answers. By guiding them, the students can see how do a problem, and remember how to do it.

Through reading this article I realized that Literature is an excellent way to get your students engaged and interested in mathematics. Through reading literature about mathematics in your curriculum students will be able to see how they will be, and have been, using math in their everyday lives. I also was not aware of all the different types of math literature that there were as well. This article gave many book titles and explained how they used them in the classroom.

Huber, L. L. and Lenhoff, R. S. (2006). Mathematical concepts come alive in pre-K and kindergarten classrooms. Teaching Children Mathematics 13(4), 226-231.

Curriculum Principle from Principles and Standards Book

Math curriculum is very important in a student’s life. It is the basis of how they are going to learn and gain knowledge in the classroom. One important thing about the math curriculum is that all the different topics are usually connected. This is important for students to know. They cannot learn a certain method, and then erase it from their memory when that unit test is over. "The interconnections should be displayed prominently in the curriculum and in instructional materials and lessons" (Principles and Standards for School Mathematics, 2010). Math is always overlapping topics into each other. If a student simply forgets a topic once the class has moved on this will not be beneficial for them.

Another important topic of the mathematics curriculum is that the math being taught should be worth both the students’ attention and time. “Allow students to see that mathematics has powerful uses in modeling and predicting real-world phenomena”. (Principles and Standards for School Mathematics, 2010). Math is involved in every aspect of our lives and students need to understand that. Another important topic is that math should be taught throughout all the students grade levels “A school mathematics curriculum should provide a road map that helps teachers guide students to increasing levels of sophistication and depths of knowledge” (Principles and Standards for School Mathematics, 2010). The type of math that is taught throughout a person’s schooling grades K-12, is very different and is taught in steps. Each level once again is always built on the previous level.