Allan HendershotEDE4944 11/4/2015

Criterion #1: Background Leading to Inquiry/Statement of Wondering

Much of the data I have gathered consists of informal field notes and interviews with my CT. My initial focus was on behavior issues, classroom procedures (transitions), and challenges with following written and verbal directions. I gathered demographic data on each student along with their current DRA results. In addition, I collected and analyzed data directly related to my inquiry which initially was based on classroom management and behavior. Data collected included notes taken during and after discussions with my CT and notes taken while checking homework or test results. The analysis of the data made me realize that the root cause of these issues might be more than just surface behaviors.

Data which led to my wondering

Field notes taken during a test tracking time on task.

Field notes taken during a lesson demonstrating the use of nonverbal cues to redirect behavior.

Field notes taken after a discussion with my CT about the class library.

Student demographic data along with their last DRA results from their previous schools.

Current DRA results and math test scores. An example of the mid chapter test which

required minimal reading.

Many of the students in my class struggle with following directions. In particular, they have difficulty with this during math lessons and when taking tests. Initially I suspected this might be a result of the students simply not knowing what was expected of them. Third grade is academically more rigorous and the work is more challenging than what they had been accustomed to. After further observation, I have come to suspect that this has more to do with their reading level then with their ability to follow written instructions. While testing, especially in math, students have asked me on numerous occasions to read words or entire questions to them. Many students in our class are not yet reading at grade level, which is evident after analyzing their DRA results.

Figure 1: Student demographic data

Figure 2: DRA results and test scores.

Allan HendershotEDE4944 11/4/2015

Claims

There is a correlation between a student’s reading level and their performance in mathematics.

This relationship is evident when looking at their DRA scores and math scores. For example, on average the mid chapter test scores were significantly higher than those on the final unit test. Although the unit test covered more material than the mid chapter checkpoint, the main difference was the amount of reading required on each test. The mid chapter checkpoint required very little reading, while the unit test consisted almost entirely of word problems. Without exception, every student achieved higher scores when required to do less reading.

There is a correlation between a student’s reading level and their behavior during and after testing.

During and after testing, many students become restless and begin fidgeting or acting out. This has been especially prevalent among those students who struggle with reading. I have recorded student behavior during and after testing using a simple checklist. Every time a student is off task I add a check, while noting who is most frequently causing distractions. In many cases the students who finish first,

cause the most distractions, and achieve the lowest scores in math are also those with the most significant reading challenges. I have spoken to my CT regarding this issue and she has arrived at the same conclusion. We have noted that many students will return to the classroom library several times after they complete a test. They will select a book, read for a short time and get back up to select another book. When I interviewed my CT about this, she stated that because many of her students are below reading level, they are struggling to find a book which is “just right.” She has been reorganizing and restocking her class library with books more suited to the needs of her students. She has researched the Lexile score of each book and color coded them accordingly. The effectiveness of this plan cannot be evaluated until additional data has been gathered. Here is a link to my initial thoughts on this issue: http://allanhendershot.weebly.com/teaching-webspace/blog-5

Figure 3: Sample of mid-chapter checkpoint test.

Allan HendershotEDE4944 11/4/2015

Both of my claims intersect with behavior and classroom management, specifically with FEAP 2a and 2b. Also, there are connections with FEAP 3h and 4a. Initially my intention was to focus specifically on classroom management and behavior; however, I have come to realize that managing a classroom and student behavior is closely linked to the content, in this case mathematics, being taught. If instruction is to be successful it must be informed by careful analysis of available data.

My Wondering

How do strategies designed to increase fluency affect student achievement on math assessments?

Criterion #2: Literature Summaries/Examining the Research

Learning Math Vocabulary. Integrating literacy and math: Strategies for K-6 teachers

Chapter 6 from Integrating literacy and math: Strategies for K-6 teachers by Ellen Fogelberg describes how to explicitly teach math vocabulary. The focus is on how to create opportunities where it is necessary for students to use mathematical terms in a clear and precise manner which demonstrates their thinking process. In order for students to gain a deeper understanding of mathematical concepts, it is necessary for them to connect appropriate academic terminology to their own experiences. This includes expressing mathematical concepts both visually and linguistically. Many techniques are outlined such as concept sorts, word diagrams, word association games, and vocabulary notebooks. The author contextualizes each strategy by describing authentic classroom scenarios.

Interviews

Due to the paucity of published information available on my inquiry, I have decided to interview four teachers at Lamb Elementary: two third grade teachers, and two second grade teachers. Because of time limitations, the interviews will be fairly short and focus mainly on their general opinions regarding this subject and the strategies they use, if any, to promote mathematical literacy fluency.

Below is a copy of the interview I conducted. The actual interview notes can be viewed on my blog here.

1. How long have you been teaching?

2. What grade are you currently teaching?

3. Do you see a correlation between math achievement, especially in relation to standardized testing, and reading level?

4. Do you feel that the reading level represented in student homework, class work, and testing aligns with the reading level achieved by the majority your students?

5. Do you feel that the emphasis on reading during mathematical assessment places too much of a cognitive load on students?

Allan HendershotEDE4944 11/4/2015

6. What evidence, formative or summative, could you point to that supports your opinion?

7. Do you feel that the line between assessment for reading and assessment for math has been blurred? If so, to what extent?

8. What strategies would you recommend/use/like to use in your classroom to improve reading fluency in mathematics?

I intend to incorporate one or more of the strategies recommended by the interviewees into my connected lesson plan.

The Science Behind i-Ready's Adaptive Diagnostic

In The Science Behind i-Ready’s Adaptive Diagnostic the authors outline how the i-Ready software platform utilizes adaptive assessment rather than fixed form assessment to gauge student achievement in mathematics. Adaptive assessment allows the instructor to identify trends in student learning not only from one unit to the next but from year to year, encompassing the student’s entire academic career. Each question or activity, which is read to the student, assesses multiple skillsets. When a student fails an evaluative task, new activities are dynamically generated which can be used to identify areas that require further instruction. Reading complexity is based on standard Lexile measures and is dynamically tracked and adjusted according to the needs of each student.

Vocabulary Instruction in Mathematics

Vocabulary Instruction in Mathematics by Margaret E. Pierce and L. Melena Fontaine discusses how a student’s mathematical vocabulary impacts achievement both in the classroom and on high stakes standardized tests. They propose that utilizing best practices for teaching vocabulary combined with detailed analysis of technical and nontechnical terms on standardized tests will increase achievement in mathematics. This process is outlined in the following three steps: first, identify math vocabulary, second, use research based principles for vocabulary instruction, and third, analyze the vocabulary used on standardized tests. When combined, the data gathered from each of these steps can be used implement a plan which combines practices from literacy and math instruction.

Strategies That Work Teaching Comprehension for Understanding and Engagement

In Strategies That Work: Teaching Comprehension for Understanding and Engagement the authors, Stephanie Harvey and Anne Goudvis, explain that in order to increase reading comprehension and fluency it is essential to explicitly teach and model questioning. The process of questioning for reading comprehension is broken down as follows: reading to answer questions, sharing questions, and categorizing questions. Each process is explained in detail with special emphasis placed on categorization through the use of sticky notes or think marks. Several strategies are also suggested such as question webs, word sorts, and anchor charts.

Allan HendershotEDE4944 11/4/2015

The underlying theme throughout the research listed above, including the interviews, indicates that reading comprehension and fluency is directly linked to student achievement in mathematics. Teaching vocabulary, whether specifically related to mathematics or literature, requires explicit instruction which makes deep, meaningful connections to student experience, encourages high order questioning, and requires students to use mathematical terminology both linguistically and visually. Strategies specifically designed to increase these skills will have a direct impact on how well students perform in the classroom and on high stakes standardized tests. I intend to implement several of these strategies in my connected lesson plan. Specifically, I intend to adapt word sorts to mathematics.

Criterion #3: Formative Data Collection and Analysis

Because my inquiry is based on the possible connection between mathematics performance and fluency, I have been collecting i-Ready data. The i-Ready software platform provides formative, interactive, real-time response and assessment data based on student performance. The software also reads all of the questions to the student thus removing the cognitive load associated with typical paper and pencil assessments. I have selected four students who struggle with math and reading. To the right are some of the baseline results from their first assessment using the i-Ready software.

The current DRA results for these students are 20, 28, 24, and 24. Their mid-chapter one math checkpoint results are as follows: 87, 78, 87, and 65. This test required minimal reading and was manly computational. The unit 1 test, which consisted mainly of word problems, resulted in the following scores: 50, 57, 38, and 50. Both covered essentially the same mathematical material. If the second test was the only assessment used to gauge math performance it would provide artificially low results.

The i-Ready data gives all four students an overall placement of level 2, although it is noteworthy that they range from the highest level two score to the lowest level two score in the class. Whether or not there is a correlation between these results and those provided by the pencil and paper tests remains to be seen and will require additional data.

Allan HendershotEDE4944 11/4/2015

In addition to DRA data, i-Ready data, and test scores, I also collected data in the form of vocabulary terms pulled from several math lessons. My goal was to discover the math terms being used during these lessons which could then be analyzed and incorporated into a teaching strategy designed to increase fluency. While collecting this data I was also taking into account the needs of English language learners. Quite a few of the vocabulary terms listed have very different meanings when defined in a mathematical context.

During one thirty minute math lesson I was able to collect over 70 vocabulary terms specifically related to mathematics used by teachers and students. Many of these are likely to be confusing to a student new to the English language.

This vocabulary data, along with evidence taken from interviews, i-Ready results, DRAs, and test scores was used to create a math based word sort focusing on the specific vocabulary used during class, on student tests, and in student homework.

Criterion #4: Taking Action Through Connected Lesson: Use of Data to Drive Instruction

The purpose of the first lesson was to teach students how to use vocabulary within the context of mathematics. In this case the focus was on area and perimeter; addition, subtraction and multiplication; or both. To achieve this I created a word sort activity based on vocabulary data gathered from homework, previous lessons, and previous quizzes. The goal was to have students appropriately sort a list of mathematical terms related to the previously listed concepts. Aside from the content standards covered in the lesson plan, the underlying objective was to encourage students to think beyond the numbers and formulas and scaffold the vocabulary to mathematics in a more meaningful way.

Figure 4: Here is the word sort from my first lesson.

Allan HendershotEDE4944 11/4/2015

Content Standards

MAFS.3.MD.3.5 Recognize area as an attribute of plane figures and understand concepts of area measurement.

MAFS.3.MD.3.6 Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units).

MAFS.3.MD.3.7 Relate area to the operations of multiplication and addition. MAFS.3.MD.4.8 Solve real world and mathematical problems involving perimeters of polygons,

including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters.

Essential Understanding

What is the difference between area and perimeter? What words or phrases in word problems help me decide to solve for perimeter or area?

Objectives (Students will be able to)

S.W.B.A.T: Sort vocabulary related to area and perimeter into appropriate categories. S.W.B.A.T: Transfer their understanding of vocabulary terms related to area and perimeter to

real world word problems. S.W.B.A.T: Identify the appropriate operation (multiplication, addition, or subtraction) and the

appropriate concept (area or perimeter) in various word problems.

Data was collected as field notes, before and after the lesson, digital photos of their word sorts, and graphic organizers completed after the word sort activity. Although the students were able to sort the vocabulary terms correctly, it was evident that there were too many categories. The focus of this lesson was area and perimeter. To increase clarity in the next lesson, I eliminated the categories for addition and multiplication and had the students sort the vocabulary for those ideas into just three groups: area, perimeter, or both. This made it easier for the

students to see the connection between area and multiplication, and perimeter and addition. I also added additional vocabulary used by the students themselves during the discussion after the activity, such as cover, inside, outside, top, and bottom. These words were not included in the initial word sort.

Figure 5: Here is the word sort from my second attempt with only three categories.

Allan HendershotEDE4944 11/4/2015

In addition to the changes listed above, I also changed some of the numbers used on my graphic organizer. My intention was to focus on the concepts rather than the calculations. To that end I created several word problems related to area and perimeter using vocabulary from the word sort. I felt the actual math was relatively simple. I was therefore quite surprised to discover that one of my word problems involved numbers too large for the students to easily multiply. They were spending an inordinate amount of time trying to diagram the area of an object which was 18 by 24 inches. When I taught this lesson again I used smaller numbers. This group had not yet learned to multiply by two digits.

The first time I taught this lesson I divided the students into two teams. Each team received a predefined selection of math terms to sort. My intention was to have each team analyze and justify their choices through group discussion once the activity was completed. For the most part, this worked out

quite well; however, it was difficult for myself and the students to keep track of their individual selections. To improve the activity for the next lesson I color-coded the vocabulary terms they were to sort by adding a red or blue dot to each card. This enhanced the group discussion after the sort because it was easy to identify the cards placed by each team.

Criterion #5: Findings from the Inquiry.

To assess student learning I relied on formative data gathered from the word sort and from the conversation between the students after the activity. I captured a digital image for further analysis after the lesson. I also gathered summative evidence from the graphic organizer. I wanted the students to work cooperatively when sorting the vocabulary.

Claim: Students were able to make meaningful connections between math related vocabulary and underlying mathematical concepts.

I wanted the students to make the connection between addition and perimeter and multiplication and area. The pictures from both word sorts, along with observations made during their conversations, suggest that the students were able to successfully make this connection. For example, one group placed the term square in the both category. When asked why they made this decision the

Figure 6: My graphic organizer before modifications were made.

Allan HendershotEDE4944 11/4/2015

team leader stated that it was because a square has both area and perimeter. The other team also made a similar observation. They placed the term rectangle in the both category as well.

Claim: Understanding of area and perimeter increase with fluency in math related vocabulary.

By applying research based methodologies for teaching fluency to mathematics I was able to promote productive discussion and create a deeper understanding of the concepts of area and perimeter. In this case, much of my evidence derives from observations made during the group discussion portion of my lesson. For example, once the students made the connection between terms such as square units and area, or inches and perimeter, they began using these terms correctly in their conversations. In particular, the second time I taught the lesson when they were discussing possible solutions to the problems on their graphic organizers, they were using the vocabulary from the word sort to justify their thinking. One example of note is when one student explained that their group should find the area instead of the perimeter because the problem asked for the number of square feet. He said that squares have an inside and that inside means area. Both groups readily agreed with this reasoning. Their increased fluency with terms such as square feet allowed them to quickly reach the correct consensus.

Claim: improving fluency in math related vocabulary will increase student engagement and reduce behavioral problems.

After my first lesson, I watched the video and noted the number of times a student appeared to be off task. I also noted the number of times vocabulary from the word sort was used correctly. My initial impression is that as fluency increases, off task behavior decreases. The first time I taught the lesson I noted 12 instances of off task behavior, and 23 instances where students used vocabulary from the word sort correctly and in context. The second time I taught the lesson there were only 7 instances of off task behavior and 38 instances where students used vocabulary from the word sort correctly and in

context. I suggest that the improved fluency in math related terms directly resulted in an increase in their use during group discussion. This in turn significantly reduced off task behavior.

Criterion #6: Reflection on Learning Through Inquiry.

If I have learned one thing this semester it is that teaching is more than just theory and planning. You have to be flexible and creative. Your lesson may not go the way you intended, or something may come up which disrupts the sequence of events you had planned. There is nothing more frustrating than crafting what you thought was a brilliant lesson, only to have it completely disrupted by

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Allan HendershotEDE4944 11/4/2015

a fire drill or some other event. Maybe the technology you intended to use is not working, or the students are stressed out and uncooperative due to a lengthy test. You have to be adaptable and aware at all times.

In order to be flexible and creative you need to know your students and be aware of their needs as learners. The students in my classroom differed in age, ability level, socioeconomic background, and English proficiency. You cannot teach one way. You have to differentiate your instruction for every lesson if you are going to reach every student.

The majority of the students in my class are below grade level in reading, and as a result they are struggling in mathematics. Most of their math instruction requires a high degree of traditional literacy, and as a result their grades suffer. Their assessment results for math are artificially low due the cognitive load placed on them during instruction and testing. The implications are far reaching. Many of these students already have a less then positive outlook towards their education. Students who once would have said math was their favorite subject now feel left behind and inadequate.

If we are to overcome this issue, we as educators need to truly differentiate for our students. To truly assess for mathematical ability we need to connect research based strategies for teaching fluency with math instruction. For my part, this means I will have to change the way I teach math. I intend to explicitly teach math vocabulary and use methodologies which are designed to improve fluency and reading comprehension.

My New Wondering

How will strategies designed to improve reading comprehension affect student performance on math assessments?

Criterion #7: Assessment Issues for ELLs.

To differentiate instruction for English language learners I have incorporated the following items into my connected lesson plan.

Spanish to English dictionaries will be made available. Key terms and definitions will be listed in both English and Spanish. Instruction will be differentiated by using hand gestures (pantomime) and diagrams to explain

key concepts. I will provide additional demonstration during the lesson and during group work. I would, if possible, pair each ELL with another student who speaks their language at a more

advanced level. If possible, I will provide access to a translation application such as Google Translate.

To differentiate assessment for English language learners I would do the following.

Students may use a translator. Answer questions orally with yes/no questions. Students my use drawings, diagrams, or manipulatives to explain their thinking.

Allan HendershotEDE4944 11/4/2015

References

Fogelberg, E. (2008). Learning Math Vocabulary. Integrating literacy and math: Strategies for K-6 teachers. New York, NY: Guilford Press.

The Science Behind i-Ready's Adaptive Diagnostic. (2014, September 2). Retrieved November 2, 2015, from http://www.casamples.com/downloads/i-Ready-Diagnostic-Position-Paper.pdf

Pierce, M. E., & Fontaine, L. M.. (2009). Designing Vocabulary Instruction in Mathematics. The Reading Teacher, 63(3), 239–243. Retrieved from http://www.jstor.org/stable/25615813

Harvey, S., & Goudvis, A. (2007). Strategies that work teaching comprehension for understanding and engagement (2nd ed.). Portland, Me.: Stenhouse.

Hendershot, A. (2015, November 9). First Three Interviews. [Web log post]. Retrieved from http://allanhendershot.weebly.com/teaching-webspace/first-three-interviews