I have learned …

25 Oct

Students aren’t kidding when they ask, “When will we ever need to know this?” In How the Brain Learns Mathematics, David Sousa suggests that students need a reason to move information from short-term memory to long-term memory. What opportunity do we give our students to reflect on what they are learning and why during class?

Many teachers give Exit Tickets, which can give teachers good information about what students have learned. However, I’ve observed many exit tickets that are more useful for teachers than they are for students. If the exit ticket requires a calculation, when do students find out whether what they’ve submitted is correct? Immediately? Or the next time class meets? How many students then complete homework using wrong ideas?

Exit Tickets can be good formative assessment. In fact, Sousa also notes that closure in a lesson shouldn’t be students packing up their backpacks and walking out of the door. Closure needs to be a cognitive process – students need to think about what they have learned and what questions they have, connecting what they have learned in class today with what they have previously learned and maybe even to what they will learn. Exit Tickets can provide students an opportunity to cognitively think about what they are learning.

My question is what types of formative assessment are we using throughout the class period, instead of just at the end of class?

Are you familiar with Dr. Sousa’s brain research on the Primacy/Recency Effect? In essence, it shows that we remember best what we learn first in a learning episode; we remember second best what we learn last in a learning episode; and we remember least what’s in the middle of the learning episode. Think about how the typical math class has been set up. Students come in, and teachers go over homework (prime learning time). At the end of class, students practice (second prime learning time). In the middle of class, teachers teach the new material for the lesson (least prime learning time).

His research shows that 20 minutes is the ideal length for a learning episode. I teach on a block schedule, and so I find that I must be deliberate about planning shorter (20 minute, when possible) learning episodes within the block.

We were finishing up a unit on Angles & Triangles in geometry earlier this week. We begin each class with an opener of questions that students work through with their teams. I collect their responses, show them the solutions, they try to correct misconceptions with their teams, and then we talk all together about any remaining misconceptions. After the opener (first learning episode) each day, students glance through our learning goals for the unit so that they can think about what they know and what they still need to know.

photo 1

Learning goals:

I can use inductive and deductive reasoning to make conclusions about statements, converses, inverses, and contrapositives.

I can use and prove theorems about special pairs of angles. G-CO 9

I can solve problems using triangles. G-CO 10

I can prove theorems about angles in triangles. G-CO 10

I can solve problems using parallel lines. G-CO 9

I can prove theorems about parallel lines. G-CO 9

I can solve problems using congruent triangles. G-CO 8

I can explain criteria for triangle congruence. G-CO 8

Because it was the last day of the unit, I asked students to answer a Quick Poll letting me know what they have learned and what they still need to know. The more I use “I can” statements for learning goals, the more I notice that they give us a common language for talking about what we can already do and what we can’t do yet.

photo 2Screen Shot 2014-10-20 at 10.00.30 AM

i have learned that i can solve problems using triangles, i still need to know how to prove theorems          1

i still need to touch up on the statemfnts and postulates            1

A.) I have learned to make conclusions, find the measures of angles, and etc..

B.) I still need to know the process in constructing parallel lines on the calc. in greater detail           1

about vertical angles            1

i have learned parrell line

i still need to know alot        1

i still have trouble ex triangle congruences           1

1.i learned prove theorems about special angles

2.i need to work on inductive and deductive statements, theorems about angles in triangles           1

i have learned conditional statements. i still need to go back over them                       1

learned how to prove why things are what they are

still need to know how to correctly prove anything from a given           1

i have learned the conditional statements

CO9 G-CO10 G-CO9,8,8

i need work on the true false charts           1

I have learned how to construct parallel lines using a point.      1

L symbolic logic

NTK proofs    1

how to find exterior angles of triangles           how to form theorems   1

i learned how to do ratios in a triangle.

need to know how to prove theroms          1

i have learned more about parallel lines cut by a transversal i still need to know more about constructing my own proofs         1

i learned about the types of hypothesis. i still need to know the different angle terms.          1

i have learned how to work with ratios.

i stll need to know how to form theorms on my own.       1

I have learned converse, inverse, conditional, and contrapositive statements. I need to learn when to use certain postulates in order to complete proofs.            1

I have learned how to prove statements using postulates. I still need to know how to explain criteria for triangle congruence.  1

i can prove theorems about angles in triangles. explain criteria for triangle.   1

how differemt types of angles are equal anb the different type of statements

i need to know the difference between converse inverse and contrapositive statements      1

learned conditional, converse, invese, and contrapositives.         1

I have learned how to solve problems using triangles. I still need to know how to do well on tables.           1

how to construct parrelel lines

how to write a hypothesis and conclusion in its different forms and determine their truth value    1

how to identify logical statements

how to do proofs       1

i need to work on converse inverse conditional contrapositive   1

i have learned how to construct parallel lines.

i still need to know how to prove the truth value of a statement.           1

learned-how to construct parallel lines

need to know-idk      1

i have learned to solve proplems using parallel lines. i still need to learn how to prove problems.   1

what aternate interior angles are;

how to figure out truth talbes.        1

i have learned if p then        1

I took the information about what students still need to know and used it to structure the rest of the class period, instead of just going through review problems in the order I happened to put them together.

A few years ago, Jill Gough and her colleagues experimented with students and faculty taking a brain break every 20 minutes to tweet what they are learning … you can read more about it here.

What will you do to ensure that you are maximizing the learning episodes in your classes?

And so the journey continues, with thanks to @jgough for making me reflect on how often I do formative assessment throughout a class period.


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