Assessing Math Misconceptions

The first problem is a tap-on-the-mistake type. Students need to analyze the projected procedure and find the mistake (if there is one). Recognizing math misconceptions is a great exercise.

– Task 1: Tap on the Mistake –

With tasks like this, everyone has the opportunity to do productive mathematics. If a student don’t know how to solve an inequality or where to start, they can evaluate the projected work. Everyone gets to apply their prior understandings of mathematics to this problem.

The fact is, your students might not catch this mistake. It is a subtle and often forgotten rule that dividing or multiplying an inequality by a negative requires flipping the inequality. If your students ask why this rule is true, you can tell them to think of it as multiplying each side by -1 and then dividing each side by 4. Inequalities are like unbalanced scales. One side is heavier than the other. When you multiply each side by -1, you are changing all negatives to positives and all positives to negatives, this means the scale will reverse. If one side weighed 10lbs and the other weighted 2 lbs the side with 10lbs is lower. Multiplying each side by -1 means the low side now weighs -10lbs (think of it as 10lbs worth of upward force from balloons). The other side is now -2lbs. 10lbs up will pull more than 2lbs so the side with 10lbs up is now higher. The scale has flipped so the inequality needs to flip.

Discussions about Math Misconceptions

Some of your students will likely choose the correct answer, and some will likely “choose no mistake was made”. Now is when the sneaky and magical power of Woot Math shines! Deselect the reveal answer button to reveal student responses as a heatmap without revealing who was correct.

– Uncheck Reveal Answer–

Some of your students might no think there is an answer, some (hopefully) got it right, and some may have chosen another place in the work. Those who got it wrong may have been guessing or may be going off of a juicy misconception… aka: a productive learning moment. For more on the value of learning from mistakes, check out Woot Math’s CEO, Krista Marks, Ed Surge article on Aha moments.

After you click show results, your heatmap might look a little something like this:

– Task 1: Heatmap of Student Responses –

Small Group Discussions

This is a great opportunity for students to discuss the problem, either as a whole class or in small groups. You can ask the students to come to a consensus as a group. This is where another one of our favorite features comes in handy. With the “assign groups” button, Woot Math automatically groups of 2-6 students. You can choose to generate these groups based on if they put the same answer (homogeneous), a different answer (heterogeneous) or at random

– Student Grouping –

With heterogeneous grouping by answer, each group should have someone who got it right (as long as you have enough students getting it right). Now, each of the groups is set up for success. Woot!

Get started by previewing the activity right now with the link below. Or, login to wootmath.com and search for Warm Up: Modeling with Linear Systems in the Shared Gallery.

Visit our page on formative assessment for more on how to use these strategies in your classroom.

Tap an Image Error Identification Weekly Woot

This week we have a short post talking about how to leverage the tap an image task type in Woot Math Polls to help promote error detection and the standards for mathematical practice.

This poll focuses on slope intercept form and is aligned to HMH module 6 lesson 1. It can be found using hash tag #hmh or #hmh6.1 if your school uses HMH, this is a great way to search for other tasks aligned to this publisher.

Task #1
The first task in this poll asks students to tap on a mistake in the reasoning. There are two mistakes, this is intended to help facilitate discussion among the students.

– Task 1: Tap on the Mistake –

After everyone has posted their responses you can reveal student answers without showing who is correct (deselect reveal answer).

– Toggle Off Display Work –

Your student work would look something like this:

- Heat Map of Student Responses -

This would be a great chance for a little small group discussion. Students can talk about why they chose what they did, if they think there is another correct answer, if they want to change their answer and what they think their peers who answered differently were thinking. To help facilitate this, the next task is the same as task 1 but with discussion questions in the scratch pad. After students are done discussing their responses you can have them try the task again. If everyone aced task 1 you can always skip task 2.

These tap an image, error detection problems are great for working on the Common Core Standards for Mathematical Practice, particularly:

CCSS.MATH.PRACTICE.MP3 Construct viable arguments and critique the reasoning of others.
CCSS.MATH.PRACTICE.MP6 Attend to precision.

Students have the opportunity to look for errors and make arguments for why something might be an error. They also can argue why someone’s choice was or was not correct.

This practice of writing down a solution to a problem with errors, taking a picture and making it into a poll is generalizable to pretty much any subject in math or even other subjects. I prefer having multiple mistakes since they tend to lead to better discussions but examples with single mistakes work well too.

This poll shows us how we can use tap an image tasks to get students reflecting on their procedures for solving a problem.

Get started by previewing the poll right now, or login to wootmath.com and search for Tap an Image Error Identification in the Shared Gallery.

Preview the Quiz

Visit our page on Formative Assessment for more information on implementing these strategies in your classroom.

Stay tuned for next week’s post!

algebra, discourse, error identification, Formative Assessment, MP3, MP6, Weekly Math Poll

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Tag: algebra

Math Misconceptions and Productive Discourse

Assessing Math Misconceptions

– Task 1: Tap on the Mistake –

Discussions about Math Misconceptions

– Uncheck Reveal Answer–

– Task 1: Heatmap of Student Responses –

Small Group Discussions

– Student Grouping –