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Math Standards Taught in Lesson (North Carolina Standard Course of Study):

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Math Standards Taught in Lesson (North Carolina Standard Course of Study):

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NC.5.NF.1:

“Add and subtract fractions, including mixed numbers, with unlike denominators using related fractions: halves, fourths and eighths; thirds, sixths, and twelfths; fifths, tenths, and hundredths.”

• “Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers.”

NC.5.MD.1:

“Given a conversion chart, use multiplicative reasoning to solve one-step conversion problems within a given measurement system.”

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General Layout of Mrs. Gilbert's Math Lesson and Connections to ED 311 Material:

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General Layout of Mrs. Gilbert's Math Lesson and Connections to ED 311 Material:

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Mrs. Gilbert implemented this lesson with a presentation in Google Slides. Mrs. Gilbert started this math lesson with a review. Every day she starts off her math lesson with a "Problem of the Day." This was the story problem: "Kylie needed 4 meters of yarn to complete her project. But the yarn was only sold in centimeters. How many centimeters would she need to equal 4 meters?" Before the students began working on the problem, she asked her students the following question: "Remind us, what does it mean to convert?" (Lower-level demands (memorization)). She then had student volunteers answer the question verbally. She then gave them a conversion chart to use for this problem (Lower-level demands (procedures without connections)). Once they worked out the answer on their own sheet of paper, they typed answers in the Google Meet chat. She had only a couple of her students respond.

She then presents the learning target of the day on a slide. She read off the learning target. She explains to them that they should achieve this learning target by the end of this lesson. The learning target was, "I can use benchmark fractions to estimate sums and differences." After this, she asks her students, "What are benchmark numbers?". Some of her students then proceeded to answer this question verbally. Her students seemed to have a clear understanding of what benchmark numbers are (Lower-level demands (memorization)). Mrs. Gilbert proceeded to present a slide that says, "When you count by tens or hundreds, those are benchmark numbers."

Then, Mrs. Gilbert introduces a Benchmark Activity they will be doing in breakout rooms. She provides explicit instructions on what they are supposed to do for this activity. It is good that she had her students take part in an assignment because they are a good tool to see any individual or even group needs (Neill, 2009). She shows them the Jamboard they will be working on (each breakout group has their own slide to work on on the Jamboard ). She tells them that they will work with twenty fractions, and as a group, they will figure out if each fraction it's closer to 0, ½, or 1. They also had to support their answer with a number line or model on the Jamboard (Higher-level demands (procedures with connection)). They put these fractions in a chart with 3 columns labeled "closer to 0", "closer to ½," and "closer to 1". She gave very explicit instructions, a great classroom management strategy (Tomilinson & Imbeau, 1999). They had about 25 minutes to complete this task. Mrs. Gilbert is able to access their answers on the Jamboard and took note of who was in each group. This is an example of a formal assessment because she will use the answers on the jam board to see how well her students understand the material (Torres).

Once all the groups finished this task, they returned to the main room. She called on a couple of fractions they worked with and asked for volunteers to tell the class what their answer was (if it was closer to 0, ½, or 1). Once the students answered, she asked the following questions that were presented on the slide: "What do you notice about these fractions that are all close to 0?" (Higher-level demands (procedures with connections)). The students who answered had some accurate ideas. She then proceeded to write down "rules of how to determine what is close to 0, ½, or 1" without the student's input (Lower-level demands (procedures without connections)). She has her students write down these rules in their notebooks. Then she proceeds to explain why what they just learned is important to know (Higher-level demands (procedures with connections).

Mrs. Gilbert didn't seem to make room for individual and group needs, which is also an effective classroom management strategy (Tomilinson & Imbeau, 1999). In terms of validity, If a test is valid, it ensures that an assessment correctly measures out what it's exactly supposed to measure, causing the results to be reliable and an accurate measure of a student's knowledge. This assignment doesn't seem completely valid since it was group work and engaged only a couple of students in each group. This only shows the strengths and weaknesses of certain individuals and not all the students (Witte, 2012)

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Levels of demand (Math Chart)

Lower-level demands (memorization):

A task that only requires one to use their previous knowledge and memorization, they don’t have to go through a procedure to solve this task.

Lower-level demands (procedures without connection):

A task that requires a student to take on a specific procedure doesn’t require them to use their critical thinking skills and have a real understanding of what they are doing.

Higher-level demands (procedures with connection):

A task that involves students using a procedure that requires deep thinking and understanding. It gives students a general idea of how to go about this task, explicitly or implicity.

Higher-level demands (doing mathematics):

A task that requires students to engage in complex tasks that don’t have explicit instructions on how to do it. For the students to solve this task, they have to understand why mathematics plays out and why the procedures they take on work.

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Chart of Mrs. Gilbert's Levels of Cognitive Demand: 

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Chart of Mrs. Gilbert's Levels of Cognitive Demand: 

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Instead of having the students work in small groups on a jamboard, I would have my students work individually. I would give my students the following assignment after giving them the same lecture Mrs. Gilbert did:

-I would give them a worksheet that has a chart with the same 3 columns Mrs. Gilbert did, fractions closer to 0, ½, and 1. Link to the worksheet: https://docs.google.com/document/d/1etC80tbOdSXDbstji_FlAxfCXCzHzE_GoMfE_RkvIaY/edit

-I would then tell them to come up with their own 4 benchmark fractions for each column and draw each fraction in any way they want (ex-> a pie, drawing out blocks, etc.)

-I would also tell them to write down any observations they have made about the fractions closer to 0, ½, and 1.

-I would give them about 20 minutes to do this task.

-I would then ask for volunteers to share some of the fractions they came up with and how they decided to draw out the representation for these fractions, and any observations they wrote down.

-I would use these worksheets as formal assessments. I would use these worksheets as an exit ticket. This would review the students' work on this assignment later to provide them with useful feedback. I would also review their work to see how to better my future instruction (Torres). I feel that this formal assessment has a highly valid construct since I believe it measures what it's supposed to (Witte, 2012). I believe it measures how much my students know about comparing benchmark fraction and their values.

I would implement this high-level demand (doing mathematics) task because it allows me to see how understanding the students are of this material. By them coming up with their own fractions for each column with their own drawings representing the fractions, it allows me to see if they have a deep understanding of the material. Writing out their own fractions allows me to see if the students really understand how to compare and contrast fraction values rather than already providing them with fractions. Also, being able to draw a representation of the fractions allows them to explore different ways to represent their own fractions. Writing down observations they have made between the fractions in each column gives them the chance to see any mathematical connections they haven't made yet. I also would provide alternate forms of these assessments for students with specific learning needs (listed under the "Differentiation" section) (Witte, 2012).

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The mathematical task framework (Stein and Smith, 1986) was implemented by Mrs. Gilbert in the following way:

Tasks related to instructional materials/curricular-> When Mrs. Gilbert went over the learning target, she presented the learning target on the Google Slides. She then asks her students, “what are benchmark numbers?”, some students answer. She then shows a slide that says, “When you count by tens or hundreds, those are benchmark numbers.”

How the teacher set up the tasks-> Mrs. Gilbert introduces a Benchmark Activity and tells them they will be doing this in breakout rooms. She provides explicit instructions on what they are supposed to do for this activity. She shows them the Jamboard they will be working on (each breakout group has their own slide to work on on the Jamboard ). She tells them that they will work with twenty fractions, and as a group, they will figure out if each fraction it’s closer to 0, ½, or 1. She also tells them they have to support their answer with a number line or model on the Jamboard. She tells them to put these fractions in a chart with 3 columns labeled “closer to 0”, “closer to ½,” and “closer to 1”.

How the students took on the tasks -> The students did this task in breakout groups. The breakout group I was in only had about 1-2 students working on this task. The others were just quiet and didn’t interact.

Was student learning achieved?-> From the students who were engaged with the task, yes. For the students who weren’t engaged, it was hard to tell.

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For my students who have an intellectual disability, I would give them very explicit examples of how to do the assignment, such as showing an example of coming up with a fraction and how to draw out that fraction.

For my deaf or hard of hearing, I will print out the instructions to read off of. I will also make sure that the lesson would include much of the material written on the board or a presentation.

For my students with ADHD, I would provide them with a time frame they could work in. For example, I could tell them that they have about 10 minutes to complete the fractions and drawings and then another 10 minutes to write out their observations. Providing them with a time frame would help them stay on task.

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The Mathematical Tasks Framework. Metamorphosis (Teaching Learning Communities). https://metamorphosistlc.com/images/Resources/Handouts/Math%20Tasks/Math%20Task%20Framework.pdf.

Neill, M. (2009). A Child Is Not A Test Score: Assessment as a Civil Rights Issue. Advancement Project. file:///Users/abbyedwards/Downloads/A%20Child%20Is%20Not%20A%20Test%20Score%20(7).pdf.

North Carolina Standard Course of Study. https://files.nc.gov/dpi/documents/curriculum/mathematics/scos/current/3-5.pdf.

Tomlinson, C. A., & Imbeau, M. B. Leading an Managing a Differentiated Classroom. ASCD. file:///Users/abbyedwards/Downloads/Tomlinson%20et%20al.%20(1999)%20(1).pdf.

Torres. Assessment As an Act of Love. ACSD. http://www.ascd.org/publications/newsletters/education-update/feb19/vol61/num02/Assessment-as-an-Act-of-Love.aspx.

Witte, R. H. Validity, Reliability, and Avoiding Assessment Bias . The McGraw Hill companies. file:///Users/abbyedwards/Downloads/Validity%20Readings%20(1)%20(2).pdf.