Today was our 3rd day. We began the day with Shaw reading the EOD, followed by you working with your ThinkingPartner in the explore phase to identify a need you have, that you want to try out in the fall regarding math and SLA.

Ron's 1st session involved developing the need for multiplicative reasoning by distinguishing between additive and multiplicative, with multiplicative having the need for the equal distribution of units across a composite unit. This was illustrated with the green and yellow unifix cubes representing limes and lemons.

Ron's 2nd session involved engaging in Please Go Bring Me in order to illustrate how to help students develop multiplicative reasoning by:

1. Running to get the cubes, pushed learners to develop a composite number, and the repeated "Please Go Bring Me" forced the bringer to have a place holder in her mind that "six units" will always be the same height as the previous six. So, that composite numerocity was developed while fetching the cubes. And the fetching took place in a different part of the room.

2. Then the need for multiplicative reasoning took place when the "sender" asked the bringer to total the entire amount of towers.

Please do two things:

1. Share the needs statement that your ThinkingPartner developed for you. For example, Amanda Rossini created for me: "Ralph needs a way to bridge previous ways of using formative assessments he used when teaching 3rd grade, to the university level. He wants this his university students to become learning partners and to set learning goals."

2. Explore how you understand the difference (and how it is developed) between developing "composite numerocity" and "multiplicative reasoning"...and where your thinking is about what you need to focus on with your students.

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Replies to This Discussion

Ellis,

I appreciate your honesty.  As candidate teachers, our knowledge and understanding of students and how they learn are for the most part, all theory.  We can in theory understand how to incorporate a lot of what we learn but we won't really know what it looks like or feels like to implement these until we get into the actual classroom.  I am with you in that I'm not too sure I fully understand the differences between composite numerocity and multiplicative reasoning but I hope that as time progresses, this seed of thought that was planted from this institute will continue to grow as I become a practicing teacher.  


Ellis Anderson said:

1.

Ellis needs a way to practically and realistically implement these strategies into a real classroom as a new teacher.

2.

I'm going to admit that I don't have any concept of either. Sorry. I can't really tell you what's the difference. And I'm tempted to go down and read other's comments but then I'd be plagiarizing their ideas. The second part of this problem asks what I need to focus on with my students and the simplest answer would be to say that I need to get the concepts. I think I have time to develop these concepts. I'd like to think that this weeks workshop is planting seeds and my ideas and thoughts need more time (and probably a lot more coaching) before they produce useable fruit.

Lisa,

I really like what you said about creating a "learning community" for our students.  I remember specific classes in which teachers were able to create a sort of no fear, non judgmental learning community where I wasn't afraid to make mistakes or say the wrong answer.  These teachers that were able to do that for me in my educational career allowed me to grow the most and see the benefit in always trying regardless of result.  I think we as teachers are doing something right if our students are able to be in a place where they have no fear of being themselves and trying their best.  

Lisa Hogbin said:

1.  Joe wrote,  "Lisa needs to develop effective ways to differentiate instruction for her students that combines what the CCSS require and what her students actually need according to their ACCESS scores and background knowledge.

2.  My understanding of composite numerocity is the knowledge that a single number represents a group of objects no matter where that number appears or if the objects are not even present.  For example,  7 is 7 is 7.  That doesn't change, even though the mathematical situation may.  The student does not need to go back and recount the objects to arrive at 7.  They have the "concept of number" to know what 7 represents. 

Multiplicative reasoning can only occur when a child has developed composite numerocity.  In multiplicative reasoning one unit is distributed over another unit to produce a third unit that is different.  For example if you had 3 oranges in each bowl and you had 4 bowls, the total number of oranges would be the new unit or 12 oranges.   We developed our understanding of this today when we played PGBM with the cubes and towers.  

What hit me over and over again today was the importance of observing our students and asking them to explain their thinking to us.  I know in my past experiences, I have not done enough of this.  As I prepare to work with new students this year, this will be forefront in my mind.  I keep hearing Ron's words, "Math is reasoning."  My job is to provide a learning community where my students are willing to share what their thinking strategies are.  With my ELL students, it is especially important for me to support them with the vocabulary they need to do this.  

Hi, Maggie.

I think the second part of your needs statement (keeping kids intrinsically motivated to do math) is something that will be difficult for me to accomplish.  As mentioned yesterday during discussion, so many people, including myself , have math anxiety, so I think the first step to motivating students like these is extinguishing this anxiety they feel and providing them with encouragement and affirmation as they move through the thinking processes. 

Margaret Fairless said:

1. Share the needs statement that your ThinkingPartner developed for you. For example, Amanda Rossini created for me: "Ralph needs a way to bridge previous ways of using formative assessments he used when teaching 3rd grade, to the university level. He wants this his university students to become learning partners and to set learning goals."

Donna created the following needs statement for me: "Maggie needs a way to teach math as a third language while incorporating second language acquisition skills; also, motivating students intrinsically to do math." 

2. Explore how you understand the difference (and how it is developed) between developing "composite numerocity" and "multiplicative reasoning"...and where your thinking is about what you need to focus on with your students.

To be honest, I'm still in the process of wrapping my mind around these two ideas. From my understanding, composite numerocity is the idea that the number 7, for example, stands for a group of seven individual 1's. A person demonstrates the concept of  composite numerocity, when they do not need to go back and recount numbers they've already counted. They don't need to recount because they understand that the single established number (the composite) represents the individual parts they previously counted. Multiplicative reasoning is when someone has the ability to combine individual composite units to create another composite unit. For example, in the game presented in class, students were asked to bring 5 towers, composed of 4 cubes each. 5 and 4 are both composite numbers. Students have multiplicative numerocity when they take these composite units and compose a new composite unit. 

The biggest thing I took away from today is the fact that in order to assess learning, teachers need to focus on a students mathematical reasoning more so than the answer. Students can get to the wrong answer and still know the process and have sound reasoning. On the other hand, students can get the correct answer and have no understanding of how they arrived at the answer. Correct reasoning, not the correct answer, indicates true understanding of the concepts. In addition to changing my focus from having students arrive at the correct answer to having the students understand the process, I need to allow students to engage in discourse with each other about their reasoning. Through discourse, they may develop new ways of looking at problems, and work out issues they may have. This strategy will create a sense of community, create a collaborative learning environment, and give me insight as to the way my students are absorbing concepts I introduce. 

Hi, Mitzy.

Organizing the information so it is easily accessible is something I anticipate as a struggle for myself.  I hope to find a way to quickly access each student's information throughout the day so I can adapt my teaching  if something seems to not be working for them.  I've seen other teachers do things like this by creating flash cards on each of their students and binding them together with a ring so you can easily keep track and flip through the information when needed.

Mitzy Barnstead said:

1. Share the needs statement that your ThinkingPartner developed for you.

 

Sarah wrote for me, "Mitzy needs a way to find time to communicate with the ELL teacher to understand scores & needs of her students so she can adjust her lesson plans to better suit their needs. Also, a way to organize the new found information.

2. Explore how you understand the difference (and how it is developed) between developing "composite numerocity" and "multiplicative reasoning"...and where your thinking is about what you need to focus on with your students.

Composite numerocity is when students recognize that a number represents a group of items; such as 5 representing five  unifix cubes. This group of 5 is now a "unit" of cubes. The student can look at the unit of cubes and know it is five, and if you were to cover it with paper, they would still say it is 5 without having to count each cube.

Multiplicative reasoning is when a student can look at the unit of 5 cubes and see there are 6 "towers" or groups of 5 cubes, and be able to identify that as a new unit of 30 total cubes. The students should not have to count each individual cube, they should be able to think, "there are 6 towers of 5, so 5, 10, 15, 20, 25, 30...".

My focus with my students will be on questioning them appropriately and requiring them to always explain their thinking either verbally or written (or both). We actually started this across the subject areas last year due to the shift to Common Core in our building. By hearing their thinking, I can identify if they actually have the mathematical reasoning, or used computation without really knowing why...

1. Share the needs statement that your ThinkingPartner developed for you. For example, Amanda Rossini created for me: "Ralph needs a way to bridge previous ways of using formative assessments he used when teaching 3rd grade, to the university level. He wants this his university students to become learning partners and to set learning goals."

Shaisha needs to find way to build assessments and paln for differentiated instruction.

2. Explore how you understand the difference (and how it is developed) between developing "composite numerocity" and "multiplicative reasoning"...and where your thinking is about what you need to focus on with your students.

Composite numerocityIs the concept of counting on using a given number  and "multiplicative reasoning is the an indept understanding of the process

Ralph,

That's a good question and I was indeed thinking about what "real" and "practical" mean. Cara and I worked on Thursday to flesh out a better need statement that hopefully more concrete:

Ellis needs resources & refreshers that practically and realistically (tangible applicable further ideas etc) teach and explore strategies after and outside this workshop.

Ralph Cordova said:

Please same more about "practically" and into a "real" classroom?

Ellis Anderson said:

1.

Ellis needs a way to practically and realistically implement these strategies into a real classroom as a new teacher.

2.

I'm going to admit that I don't have any concept of either. Sorry. I can't really tell you what's the difference. And I'm tempted to go down and read other's comments but then I'd be plagiarizing their ideas. The second part of this problem asks what I need to focus on with my students and the simplest answer would be to say that I need to get the concepts. I think I have time to develop these concepts. I'd like to think that this weeks workshop is planting seeds and my ideas and thoughts need more time (and probably a lot more coaching) before they produce useable fruit.

Clearer in deed!

R

Ellis Anderson said:

Ralph,

That's a good question and I was indeed thinking about what "real" and "practical" mean. Cara and I worked on Thursday to flesh out a better need statement that hopefully more concrete:

Ellis needs resources & refreshers that practically and realistically (tangible applicable further ideas etc) teach and explore strategies after and outside this workshop.

Ralph Cordova said:

Please same more about "practically" and into a "real" classroom?

Ellis Anderson said:

1.

Ellis needs a way to practically and realistically implement these strategies into a real classroom as a new teacher.

2.

I'm going to admit that I don't have any concept of either. Sorry. I can't really tell you what's the difference. And I'm tempted to go down and read other's comments but then I'd be plagiarizing their ideas. The second part of this problem asks what I need to focus on with my students and the simplest answer would be to say that I need to get the concepts. I think I have time to develop these concepts. I'd like to think that this weeks workshop is planting seeds and my ideas and thoughts need more time (and probably a lot more coaching) before they produce useable fruit.

1. The need statement that my thinking partner came up with for me was: Cecilia needs a way to apply all of her knowledge and experiences into a classroom setting where she is in charge of the lessons, crafting plans, and management.

2. Composite numerosity is when a numeral stands in for a group of other things (objects) and multiplicative reasoning is using composite numbers to work with more than one group units. The second cannot be taught without a solid understanding of composite numbers.

Maggie stated that" Donna needs a way to assess her students in mathematics as soon as possible without allowing time constraints to keep her from getting accurate assessments on her students.

I understand that I cannot move my students on to multiplicative reasoning until they have the concept of composite number and counting on.  In the game, HFFS, students are able to continue counting on with a partner by rolling the dice and determining how far they are from the start.  If students can successfully explain how they moved and where they are on the board, they are ready for multiplicative reasoning.  In this concept, students are to count towers or groups and tell how many units are in each tower.  Students should be able to tell you how many units are in a specific number of towers, how many towers can be made by a specific number of units. When transfer of this is from concrete to abstract on paper, they are ready for the next step which is division.    I will have all the ELL students in third grade this school year and I am concerned a little about that.  I know they are at different levels in their reading, writing and math so my focus is to help them with the skills needed to exit the ELL program and get ready for their first attempt at the state test.  But first and foremost, I want to make sure that they understand the math concepts we have learned in the institute. 

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