Balanced Assessment in Mathematics Review

To recap the last couple of weeks, the group and I have been working on breaking down standards and reviewing lesson plans. This week, I will be reviewing an assessment from the Balanced Assessment Project which is a project to provide a collection of assessments that provide teachers with an understanding of a student's knowledge of mathematics. The assessment I will be reviewing is called Dot-to-Dot which applies to the standard, CC.2.2.2A.2: Work with equal groups of objects to gain foundations for multiplication.

            The Dot-to-Dot assessment asks the student to do a connect the dot activity by connecting the even numbers in a picture and connecting multiples of three in another picture. This activity allows students to work with repeated addition and practice working with equal groups in a fun, interactive fashion. Unfortunately, there is no way for us, as teachers, to tell if a student is simply counting each number one by one unless the student is totally off and did not create the picture they were supposed to create. It is more of a self-assessment activity for the students.

Lesson

Last Class Gabbie, Candace, Professor Mace and I explored the PDESAS website to gain an in sight on the standards we unpacked the week before. The standard I unpacked was CC.2.1.2.B.1  using place-value concepts to represent amounts of tens and ones and to compare three digit numbers.
Which means children must be able to understand place values in three digit numbers. They also must know how to represent tens place, ones place, and hundreds place.

The lesson I chose is 2nd grade number sense and place value. The objectives for this lesson are students will understand place value--the value of a digit depends upon its place or position in a number, and  Students should recognize the numbers 0 to 999. They will gain an understanding of the place values for ones, tens, and hundreds.

The lesson starts by giving a prompt. "Today we are going to strengthen our understanding of place value.  To do this, we will represent or show numbers in several different ways. Let’s begin with our NUMBER OF THE DAY place values and start with the number 137.  First, I will write the number in standard form.  Standard form is the usual way that we write a number.  Now I will use the base-ten blocks to represent the number.  I first look at the hundreds place.  I see that there is 1 hundred so I will use one flat.  Next, I look at the tens place and see that my number has 3 tens.  I will use 3 ten-sticks (longs) to show my number.  Finally, I will look at the ones place.  My number has 7 ones.  I will use7one-cubes.  Now I have shown the number 137 with my base-ten blocks. Ask the student to fill in the number and tell whether it is even or odd. Ask students how they determined whether it was even or odd."

I believe this is a good way to teach students place value with three digit numbers. However, I would change this lesson to have it more children based. I would have the children do the steps with me instead of the teacher just modeling it at the front board.

http://www.pdesas.org/ContentWeb/Content/Content/27965/Lesson%20Plan

Last week, Professor Mace, Gabbie, Jen, and I explored the PDESAS website and searched for lessons that related to the standard we unpacked the week before. The standard that I am working with this week is CC.2.4.2.A.4 which states; represent and interpret data using line plots, picture graphs, and bar graphs. This standard is under the domain measurement, data, and probability. 

The lesson I found that follows this standard is called How Big is a Foot? This lesson is based off of a book called How Big is a Foot? By: Rolf Muller. The essential questions for the students' to keep in mind while completing this activity are why the bed was a different size when measured by someone else's foot other than the king's and whether everyone's feet are the same size and how they can prove whether that is true or not. The students are instructed to get into groups, trace each other's feet, and cut them out. They will predict how big they think their feet are and then measure their cut out feet with their actual feet to see the length. The students will then record the predictions of how big they think their feet are and then the measurements of their feet onto a chart. The teacher shows the students' all of their feet measurements and explains how they are all different and because they are all different, they need standard measurement tools instead of actual human feet to be able to measure accurately.

This lesson follows the standard CC.2.4.2.A.4 because the students represented their feet measurements onto a chart and compared those measurements after to show that human feet are not a reliable form of standard measurement. This lesson states that it follows the standard CC.2.4.2.A.1 which states measure and estimate lengths in standard units using appropriate tools. The students were never instructed to measure their cut out feet with an actual standard form of measurement such as a ruler. The students only measured their cut out feet with their actual feet and compared that data instead of measuring their cut out feet with rulers and comparing those to the foot measuring technique. 

For the students to fully grasp the concept of measuring with standard measurement tools, they need to be able to measure their cut out feet with 12 inch rulers. A ruler is a standard measuring tool used in the US. Using the 12 inch ruler would ensure that all of their feet could be measured. They could also measure their actual feet with the rulers to see how long their feet are and whether they have different size feet or not and compare their cut out feet measurements to their actual feet measurements. 

Lesson Review

Last week, I unpacked the standard: CC.2.2.2A.2: Work with equal groups of objects to gain foundations for multiplication. It was a bit challenging because it required a bit of research to be able to understand the standard enough to accurately describe it let alone create a lesson for it. To gain a better understanding of how a standard can be applied to a lesson, I will be reviewing a lesson based on the standard I unpacked last week.

The lesson I chose is called "Skipping" which refers to skip counting equal groups. Luckily, the lesson provides a few materials that can be used in teaching this lesson: dot cards, a number line, a self-check sheet, and a script. To go about teaching this lesson, I would start by flashing a set of chips arranged in equal groups and asking my students how many chips were there. They will automatically have to start noticing patterns and developing strategies to count in new ways. I would then use the dot cards and the number line to get the students to see how the numbers move and equal number of times across the number line. After the students get the hang of that, I would pair the students up in groups of two to practice working with equal pairs on their own. They would start working with the cards faced up and determine how many dots there are and explain how they determined their answer. Then, they will turn the cards over so the dots can't be seen, and they will try to determine how many dots there are total knowing only how many dots there are on a card and how many cards there are total. After they have both become comfortable with this, they will fill out the self-check sheet.

This lesson is a good introduction to multiplication because it provides a concrete strategy that is essential in understanding multiplication, so it clearly fulfills the standard. I wouldn't change anything about this lesson. I found this to be a solid lesson.

Unpacking standards

    
     Last week we talked about "unpacking standards and what they really mean. When you just see the standard numbers and operation were not sure how to really teach that. This is what I think 2.1 Numbers and operations CC.2.1.2.B.1 means.



Domain:
       2.1 Numbers and operations

Standard:
       CC.2.1.2.B.1 using place-value concepts to represent amounts of tens and ones and to compare three digit numbers.

What does it mean?
      Children must be able to understand place values in three digit numbers. They also must know how to represent tens place, ones place, and hundreds place.

Content goals:
     Regrouping, regrouping with zeros, understanding the different place values.

Process goals:
     manipulatives such as grouping blocks, expanded notation, scaffolding, and  adding using left to right.

Unpacking the Standards for Algebraic Concepts

The last time I met with the group, we were examining and breaking down the standards in our chosen domains by determining the actual meaning of the standard, the content goals, and process goals. My domain of choice is algebraic concepts, and today, I will be focusing on unpacking the standard, CC.2.2.2.A.3: "work with equal groups of objects to gain foundations for multiplication." This standard means that the students will group things together to work towards multiplication. If I were to teach this standard, my main content goal, or conceptual goals for the lesson would be teaching my students multiplication with single digit numbers and some double digit numbers using equal groups. As for process goals, I would aim towards teaching my students how to utilize the equal groups strategy on objects, pictures, number lines, and skip counting for basic multiplication.

Unpacking Standards

Last week Professor Mace, Gabbie, Jen and I unpacked different standards in different domains. We went through three different domains and worked with a standard from each domain to try and find out what they really mean. We first reworded the standard into our own words. We then came up with a list of content goals we would want our students to accomplish when teaching this standard. Content goals are the goals that would guide the teacher to help his/her students towards understanding each concept included in the standard. The last thing we did was create a list of process goals we would have if we were teaching this particular standard. Process goals are goals that guide the teacher to help his/her students to understand how they solve a certain problem in a specific concept. It allows the students to explain their reasoning for solving a problem a certain way and how they got to their answer. This gives the teacher an idea of whether the student knows the concept and it gives the student feedback on what they need to work on or if they can move on to the next concept.

The standard I am going to unpack today is CC.2.4.2.A.4 which states; represent and interpret data using line plots, picture graphs, and bar graphs. This standard is under the domain measurement, data, and probability. This standard means that students should be able to draw/write different kinds of graphs and charts and understand the information on these different data displays. Content and process goals for this standard for second grade should include using concepts of maximum minimum to read and compare data from a variety of data displays, describe features of data such as range, mode, and median, describe parts of the data and the set of data as a whole to determine the trends in the data, interpret and construct different data displays, describe the advantages and disadvantages of using different data displays, and analyze the data to form an opinion on whether a statement is true or not to justify their opinion.

standards

Last week Candace, Gabbie, Professor Mace and I sat in our universities library to examine some second grade math text books. I was very frustrated with the lay outs of many textbooks we looked over. It was hard to find similar problems when comparing two textbooks side by side. To my surprise the teachers edition was no better than the students textbooks. They were very confusing. They had options for problem of the days, silent work, and assessments.Textbooks are ment to help you not teach the class for you. There was so much going on it was very unclear what to teach the children and what was common core.

There seems to be a very blurred line between what is curriculum and what is common core. Common core is what you need to teach per the state. There is no specific way it need to be taught that is the curriculum.

I chose the standard CC.2.4.3.A.3. Solving problems and making change involving money using a combination of coins and bills. I will be studying this standard in a second grade classroom. I hoping to come out of this study with a better knowledge on how to apply common core without the use of textbooks.

Struggling Search for Similar Standards

Looking through textbooks and trying to find similar standards in multiple textbooks is not as easy as it seems. Last week, Professor Mace, Jen, Gabbie, and I sat in the library and looked through teacher textbooks to find similar standards. We thought that it would be simple to find the same standard in each textbook but that was not the case. The standards were so vague that the lessons in each textbook were different as well and made it difficult to compare. Teacher textbooks can be overwhelming and it seems impossible to determine as a teacher what exactly to teach the students.

We felt that more inexperienced teachers would tend to rely on the textbook more than experienced teachers. This can be a good and a bag thing. When the standards are vague, the teacher has freedom to teach the lesson in a more preferred way but with this freedom, it can be difficult to make a lesson with not much to go off of and teachers may struggle with their lessons because of this.

There are standards which tell us what students at a certain grade level should know to move on in their education career. Curriculum is based off of textbooks a lot of the time so the question is how do we write curriculum based on standards not on textbooks?

The standard I chose to focus on is CC. 2.4: Measurement, Date and Probability. The grade we are focusing on is second grade. There are five different areas that are covered in this standard which includes measuring and estimating lengths, telling time to the nearest five minutes, solving problems and making change using coins and paper currency, representing and interpreting data using line plots, picture graphs, and bar graphs, and adding and subtracting problems involving length. Hopefully through my research in this study, I will learn how to base curriculum on standards and not just on textbooks.

Chaotic Curriculum Search

For years, I heard teachers complaining about the common core standards and their frustration with textbook companies, but I never quite understood where all of this frustration came from until last week. Professor Mace, Candace, Jen, and I did some standards research to see how they corresponded to mathematics textbooks, and let me tell you, it was not the best experience I have ever had. I left feeling a bit discouraged to say the least in regards to creating a curriculum and applying standards-based grading in my classroom.

The textbook companies are simply interpreting the standards and providing lessons for teachers to work with, but the standards are so unbelievably vague that you are never guaranteed to find the same lesson if you jump from one textbook to the next. We attempted to compare different textbook brands that were supposed to fulfill the same standards, but it was nearly impossible to match up the lessons even when the corresponding standard was provided. The vagueness of the standards is both a good thing and a bad thing. It gives you some creative freedom to create a curriculum that works for you, but the guidelines are so vague that they are barely helpful. For that reason, it makes me wonder how you could possibly create a curriculum that is not entirely based on a textbook but also meets the standards.

At this point, achieving that goal seems a bit far-fetched. Sure, technology allows us to acquire teaching resources in less than a minute, but there are still hours of planning that goes into a single lesson. That may not seem like too much, but imagine doing that for 180 lessons and having to edit them based on what the class needs more or less time working on. In the context of standards-based grading, this seems entirely impossible. There simply not enough hours in the day to accomplish all of these things; teachers are very busy people. I'm sure that there is another way to go about applying standards-based grading in my classroom and creating a curriculum that works well for me and my students, and hopefully, through my research, I will find out how to make that happen.