Journaling

Assessments: Setting Routines for Self Reflection

Setting Routines for Self Reflection

MJ Kinard

Assessments and Mathodology

Precision teaching is the idea that relates to the book, Visible Learning by John Hattie. The premise behind Hattie’s research is the correlation between surface, deep, and transfer learning.

The findings go on to address the influence that different aspects of the education system have on our students and the math classroom. Basically, the idea of getting the “most bang for your buck”.

Every school district, school, and classroom teacher wants a magic formula for success. With limited time and funding, how do we ensure our academic goals are being met in the math classroom?

As math teachers, how do we know if our students are learning?

Setting Routines

Setting routines are one of the cornerstones of a successful classroom. It is important for teachers to understand the difference in a compliant classroom and an environment conducive to learning.

When beginning the school year it is crucial to ask ourselves a few questions when considering routines and procedures.

  • Do your students know what they are supposed to be learning? And more importantly why?
  • Are your students benefitting from your expertise?
  • Are your students capable of connecting their learning to what they’ve already learned and are they able to see where this learning goal will lead?
  • Are your students able to manage their own learning?
  • At the end of the lesson, are your students able to hold themselves accountable for what they have learned? (leading into self-assessment)
Pictures of students during our “admiration tour”. You can see them and the work they have produced.

Self-Assessment

Self-assessment has one of the largest effect sizes for student learning (Hattie, 2009). The process of self-assessment requires several different elements implemented in the classroom.

One example of self-assessments in the math classroom is the use of Math Journals. Beyond a journal prompt containing the “content goal” teachers have an amazing opportunity to go beyond a right/wrong answer by providing students with a voice for self-reflection.

Below is an example of a pre, mid, and post year self-assessment used in a fourth-grade classroom to gauge confidence and attitude toward mathematics.

This same questioning is also used in this classroom in the aforementioned Math Journal activity. The example seen below addressed the math topic of Place Value. The students were asked to describe the value of the 8 in the number 88,888.

They could use pictures and words. The prompt was actually shared at the beginning of class as an informal discussion. Students were asked to read the prompt and think about what they already knew about place value, what they remember from previous lessons that would help them with today’s goal, if they felt like the topic was going to be difficult and if so, why?

They were given time to think about their responses and write them in their journal, then after the lesson, they returned to their journal to work on the prompt and reflect on their thoughts from the beginning of class. Once journals were complete, they were allowed to share the journals with their group.

The outcome of this part of the activity is to foster a safe space for math discourse, more importantly, mathematical talk is proven to lead to the ultimate level of transfer of learning and metacognitive awareness.

Self Evaluation/Assessment Form

Metacognition

If self-assessment is the goal and math journaling is one tool, what is the payoff? How do these techniques help spark success in our math students? Metacognition is the ability to think about our thinking (almost sounds too simple).

While it may sound simple it is the cornerstone of all actual and true learning. Metacognition happens when students practice self-reflection on their level of thinking. In addition, when students can relate this to a target it becomes powerful enough to increase understanding and motivation.

This knowledge promoted in the classroom is invaluable. As teachers, we all dream of that day when our students are intrinsically motivated. A moment in the classroom when the value of the content rises above a state standard or an arbitrary notion but becomes a self-fulfilling desire to learn and grow. But students need guidance and tools to develop their metacognitive awareness and become confident in the ability to self-question.

Formative Evaluation

Formative evaluation is the process of gathering evidence to inform instruction. In simpler terms, it is the process for teachers and students to communicate about the learning that is taking place and the direction that instruction should go. Formative evaluation should drive instruction decisions, gathering real-time data is crucial in guiding how the teacher will proceed with the delivery of the lesson.

In the book, Visual Learning, Hattie speaks of several internal questions that drive learners:

  • Where am I going? What are my goals?
  • How am I going there? What progress is being made towards my goal?
  • Where to next? What activities need to be undertaken next to make better progress?

Consequently, these are the same three questions that teachers must ask about instruction as they make adjustments based on the data they gather from students. Some examples shown below, include response cards (whiteboards), and exit tickets, journal entries may also serve as a way to inform instruction.

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Meaning of Equality

Meaning of Equality

Often we teach the meaning of equality as the equal sign indicating “put the answer.”  To prepare students for future mathematics, we need to rethink the way we communicate this representation to students.  The equal sign is too important to attach such a limited meaning, especially when students are moving to abstraction.  When moving to abstraction, it is important to use this symbol as a “reader” versus a “speller.”  What do I mean by that? Let me explain.  First, a speller sounds foreign because the student is trying to make sense of abstract symbols that they don’t fully understand. A reader connects meaning that they can comprehend while connecting the story to the symbol.

For example, when teachers record the following equation,

Meaning of Equality

Using a simple addition problem as a reader versus a speller.

 

A speller would say, “Four plus five equals nine”.

A reader would say, “Four apples and five apples is the same as saying ‘I have nine apples’” .

In the journal prompt below, we want students to see the statement as 5 and 4 is the same as 2 less than 11. If we focus too much as a speller, students see symbols as performing actions rather than relating ideas, which leads to misconceptions of the equal sign.

Less is more. Hesitate in thinking math becomes harder by creating larger numbers, rather provide depth early on using children’s intuitive understanding of basic number operations.   A simple journal entry can help assess what students understand about operations and the meaning of equality.  Once you find that a student understands the meaning of addition and subtraction, it is time to create tasks that dive deeper in understanding equality.  These task can be as simple as asking questions such as, 4 + 5 = ____ + 6.  Additional equality tasks can be found in the Algebraic Thinking and Reasoning with Numbers books (Groundwork Series) by Greenes, Carole, et al., (https://www.mheducation.com/prek-12/program/MKTSP-O8302M06.html).

In the book, “Thinking Mathematically,” Carpenter, Thomas P., et al. suggest some benchmarks to keep in mind while moving towards the conceptual understanding of equality.

  1. Establish a starting point.  What are students’ initial ideas regarding the equal sign?
  2. Mix it up.  Don’t always write equations in the form a + b = c, rather c = b + a.
  3. See the equal sign as a relational symbol. Emphasize students proving that each side is the same as the other.
  4. Compare sides without calculations. Encourage students to look for relationships without performing calculations.

 

Listen to students and be aware of where they are in the process. Encourage them to question if it is true.   If so, why is it true?  By listening and looking we may be pleasantly surprised at what we find out.

Below is student work demonstrating various levels of understanding within the concept of equality.

Spiky says that 5 + 4 = 11 – 2 is false.

Curly says that it is true.

Who do you agree with and why?

 

Meaning of Equality

This student understands how to simplify expressions but lacks applying the meaning of equality.

 

Meaning of Equality

This student is confused in understanding what it means to have expressions on each side of the equal sign.

 

Meaning of Equality

This student understands the meaning of equality. What can we ask next?

 

Meaning of Equality

This student demonstrates a shallow understanding of equality. What can we do next?

 

Meaning of Equality

This student can solve for an answer but needs practicing in mixing up the form of an equation.

 

 

 

 

 

 

 

 

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Journal Entry Place Value

Spiky was using blocks to show 304.  

When Spiky was not looking Curly took 2 rods and 1 flat.

What is the remaining value of Spiky’s blocks?

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Journaling Number Bonds

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Journaling Rote Counting

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Journaling in Grade 1 Number

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Sarah Schaefer

 Sarah Schaefer - Student Work

Correcting journals does not require lengthy comments or grades.  A simple stamp will do.
“Got It!”

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Sarah Schaefer

 Sarah Schaefer - Student Work

Correcting journals does not require lengthy comments or grades.  A simple stamp will do.
“Are you sure?”

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Journal Prompt based on misconception

Who do you agree with? Explain.

Spiky says his number 32 tens + 5 ones is the biggest.
Curly says her number 1 hundred + 3 tens + 2 ones is the biggest because she has the most hundreds.
Buzz says his number 5 ones + 3 hundreds + 2 tens is the biggest because the first digit 5 is bigger than 3 and 1.

I got this!- Student 1

Do we know how to help Student 2?

What can we work on with student 3?

Student 4 needs more concrete experiences. Maybe we have them build these numbers and edit their journal if needed? This students needs to reflect once they can see the mistake on what the error was.

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Grade 2 begining Journal Entry

Journal Entry:  Given a number write four things you know about that number.

 

How can we use this to help assess where a student is before we even begin a formal lesson?

Student 1:

Student 2:

Student 3:

 

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Sarah Schaefer

 Sarah Schaefer - Student Work

Great Day 1 journal prompt to set up structure of journaling.

What do you like about learning math?
Give 2 examples and an explanation.

Day 2:
What do you not like about learning math?
Give 2 examples and an explanation.

Great way to get to know your students. Share your results!

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