This video showed a good way to help students understand the relationship between addition and multiplication. It helps to build their number sense. Initially, the students showed they know there was a relationship but they were not exactly sure what that was. They explained methods such as using research and investigating the relationship through various other methods. I think it was interesting to see how the students became to make their models and figure out the relationship.

What I think I would do different would be to give them the materials and let them figure out how to model it. The teacher in the video explicitly showed them how to make the model and what to do. I am not sure if the students later on in the video developed their own methods or not though.

One important thing to always keep in mind when working in the classroom, no matter what subject you are teaching, is to ask open ended questions to your students. This will help them figure it out without you telling them. They can connect their previous knowledge to what they are learning now.

Similar to this was the Creative Thinking In Subtraction article. The students shared their different ways they solved the problem. As I mentioned above, I think this is a great thing to do in the classroom. There are many different types of learning styles and we need to take this into account. From my past educational experiences, I remember only being taught a concept one way. What these teachers are doing is allowing the students to find ways that work best for them. This is important to remember in my own classroom!

As I reflect on how I was taught in school my basic facts, I remember being drilled on them. My teachers used flashcards, played around the world, etc. This may be one reason why I still sometimes need to think and visualize the problem in my head before I can compute it. I think that sometimes these drill activities are okay; however only after the students really understand and can use these strategies and not just memorize the facts.

The second article I read was Three Sides, Three Corners. In this article a group of 2nd grade students were trying to describe a triangle. Most of the students could look at the set of triangles the teacher presented to them and see that they were triangles; however, there were a few students who thought they were not a “real triangle” but just in the triangle family. I think they were starting to understand the difference between different types of triangles. Through the discussion, the students began to see that all the examples shown to them were triangles, just not the traditional equilateral triangle they may have been used to seeing. The teacher had the students write a description of a triangle after their discussion. This could also be used as an assessment since you could see the student’s level of understanding on an individual basis.

I think that the activities designed for the students gave them the opportunity to begin to explore the problem on their own. It is important for students to be able to test and figure out a problem so they begin to build their schemas and knowledge on a particular concept. I also really loved how the teachers gave the students the opportunity to showcase their knowledge and their solutions they designed. It is important not only because it acknowledged their understanding, but it also allowed the students to communicate with each other. Stepping out of the lesson a bit and allowing the students to communicate and explain or ask questions to each other gives them the opportunity to learn from each other and also with this particular set of students allowed them to practice their communication skills.

I think in order for me to become a better math teacher, I will need to build my understanding of the students’ errors. It is not about finding their errors; instead it is about figuring out why they made a mistake. Asking questions and having the students’ explain their logic is a key to unlocking their misunderstanding. Errors are not a bad thing; they enable us as teachers to figure out where our students are going wrong, allowing us to find ways to put them back on the correct path. I think this is going to be my toughest challenge as a new teacher. I will not have as much background experience in figuring out why they may be making an error. I think figuring out ways in which to question the students will help me to better assess their understanding.

Since assessment is a large portion of what my job will entail (allowing me to gather information about my students’ understanding in order to guide my instruction), I feel that when a rubric or scoring of an activity/assignment is in place, a student should always receive some credit for their attempts. This is why I feel partial credit is a good idea. You don’t want to discourage a student by giving them zero points even though they tried and hopefully tried their best. As some teachers have expressed to me, they have students who are so afraid of being incorrect that they won’t answer a question or even try to solve a problem. Providing at least partial credit will in my eyes hopefully help to build their confidence in at least trying. Making an attempt at something is always better than not even trying. As I mentioned previously, making errors just allows you to understand where you are and in turn help you and the teacher figure out where you need to be and how to get there.

The school’s decision is made complex because of a number of different factors, but what I took out of this article was 3 main points.

1) Schools need to be careful about the claim of research-based. Is it really scientifically research-based? Most publishers do not go this route because it is very time consuming and requires lots of participation and cooperation with schools.
2) Schools need to look at how the material in the textbook correlates to their Stand Course of Study (SCOS), as well as how that material is presented to the students. Does the textbook cover the necessary skills in an appropriate manner. Does it fit within the school’s framework and philosophy? Are the teachers supposed to present the concept and then work through example problems or are the teachers supposed to present a problem and encourage the students to work through it based on their previously built schemas (the latter being what I perceive to be the better approach)?
3) Schools need to be careful with the incentives offered. Are you going to choose one textbook over another because you like the fact that you are getting extra materials mainly for free or because the text aligns with the curriculum and philosophy?

Schools have a tough job finding appropriate textbooks. I have not had much time to look at the math textbooks my school uses yet, but I will make a point to look at them this week. I am interested in the content, how the concepts are presented, what extra materials will be utilized and how the teachers will then use all of this.

I think it is important to remember that even though there is a SCOS and materials provides, teachers need to design lessons based on what we learned in our teaching math class. Students need to build their own schemas in order to be able to put that knowledge in their operative knowledge bank and not in their figurative knowledge bank. This leads into the second article we read this week, Parents Rise Up Against A New Approach to Math.

This article discussed how some parents are upset by the manner in which mathematics is being taught in their child’s school. I think that parents are used to a certain way of math being taught and are not seeing the bigger picture. They only see that this was the way they were taught so it must be the right way. What they may not know is what research says and how a child’s brain and thinking actually develops. They think because they memorized their facts it is what their child should be doing. They are not aware of the new strategies that have arisen, the ones that actually teach students so they comprehend the concepts. This enables students to not memorize, but instead actually learn the concepts allowing them to most likely pick up more complex concepts later on. Some parents are probably not aware of the strengths of these new techniques. I think it is important for teachers and schools to discuss the manner in which mathematics will be taught in the school. We can be the bridge that helps parents gap how they learn mathematics with these new strategies. We can explain the reasoning and then help them to understand these new techniques. I think if parents were more informed in terms of child development, current scientific research and these new techniques they might feel more comfortable with the changes. Some people do not adjust to change, especially if it means they may not understand what their child is doing, in turn meaning they may not be able to help their child at home.

From the readings this week there were the 6 points to keep in mind when designing tasks that stuck out the most to me.
1) Need to be authentic – students need to work on math in real life situations that are appropriate to the math concept.
2) Need to bake a bit challenging but within their reach – design tasks to help push students to the next level (scaffold) and ones that allow them to use higher-level thinking skills to push them further
3) Need to pique student’s interests and curiosity – students will be more willing to do the work or learn a concept if you make it relevant to them
4) Need to encourage students to grasp the concepts – how well it builds on their previous knowledge, peeks their interest and provides thought provoking opportunities will further their understanding
5) Need to take into account multiple perspectives and how the tasks interrelate with the concepts – design based on the different levels and intelligences in the classroom, multiple ways to see a solution
6) Need to design within problem solving skills – encourages higher-level thinking.

Creating tasks with higher-levels of demand will help the students. It allows them to think, reason and problem solve. I think the key is to be able to consider where your students are at, what will help to reach them and then design appropriate instruction that will enable them to think at a higher level (higher for them individually).

I am finding that the six first grade teachers I am assisting are beginning to figure out where their students are and what they will need to help further their skills. I am looking foward to working with the students and seeing how the activities the teachers design attempt to get the students to think on higher levels.

Video 1: The student is asked to tell what a square and a triangle are. From the student’s response I would say this student is functioning at a Level 1.This student is able to show Mason what a square in by drawing it in the air with her finger, but she is not able to verbally explain what makes a square a square. In Level 1, students will recognize an object or shape by its appearance alone.

Video 2: The student is asked how he can tell the object on the table is a triangle. From the student’s response I would say this student is functioning at a Level 1 but also seems to be in the process of transitioning to Level 2. This student is able to provide an explanation of a triangle (whether it is the best description or not); however, when the triangle was turned sideways or upside down, he cannot see the relationship fully. He does seem to understand that it is a triangle but maybe in a slightly different manner.

Video 3: This is the same student from Video 2. This time the student is shown another triangle (not congruent to the last). This student seems not to be sure if it is a triangle. It appears he knows that it still has a point and a straight line at the bottom (his originally explanation of a triangle), but is not sure if he is entirely correct.

Video 4: This student is asked the difference between congruent and similar triangles. She has provided an answer that shows her understanding of the concepts. She states that congruent means same shape, same size while similar means same shape, but different size. I would state from this response that the student is functioning at a Level 3. She has made meaningful definitions and sees the relationships between the triangles.

Video 5: This student is asked if the two circles on the table have the same angle. She states that they both are the same angles because they have the same degrees. She also explains that you use a protractor to obtain the degrees of an angle when she is asked. From this response, I would say she is functioning at a Level 3.

Video 6: In this video, the student is asked to sort a bunch of different blocks. The student sorts the blocks based off of the things he has made with them. He sorts them by houses and by letters (he made the letter T and O and 3 or 4 different houses). He obviously did not grasp the concept of the question, so Mason asked questions about a few objects (asking to name their shapes). For some of the shapes he provides the correct name while others he can only give their name if they were 2 dimensional. For this reason, I would say that they student is functioning at a Level 2.

Video 7: This student is asked to sort a bunch of triangles, which are not congruent. The student creates his name with the triangles and does not sort them in a “typical” manner. I would say this student is functioning at a Level 2 because he cannot see the relationship between the triangles enough to sort them, even though he sees them as some type of collection.