Being on Twitter and following hashtags like #MTBoS and #ITeachMath allows me to see classroom mathematics well beyond my physical horizons. I get to glimpse creative and engaging mathematics education around the globe. Recently I saw a couple of different ideas that I've tried to adapt and apply for myself.
Since the Nova Scotia grade 8 classes are working on integer multiplication and division, I decided to create a math mystery of my own. Another nice source of math mysteries is the book Mathematical Team Games: Enjoyable Activities to Enhance the Curriculum by Vivien Lucas.
I liked this idea because it is relatively easy to create; just a find a series of questions with unique answers. Also, students get instant feedback. If their answer isn't on the map, they know they've made a mistake. I would call this purposeful practice as there is a goal to achieve at the end of the activity. There is a reason to persevere. Once students are familiar with the activity, you could give them a blank template (or they could hand draw their own version) and they could work in small groups to make their own treasure hunt activity (and answer key) and share it with each other.
The Role of Practice
I recently read Mark Chubb's (@MarkChubb3) blog post on the role of practice in math class. He discussed the differences between "rote practice" and "dynamic practice". Rote practice involves following procedures, drill and repetition while dynamic practice involves active student thinking, playful experiences and puzzles. I think that the Mystery activity is a more "dynamic" activity than doing the Treasure Hunt activity. However, I think that creating your own Treasure Hunt activity does involve additional characteristics of dynamic practice.
I'm a fan of self-checking math activities. These activities give students immediate feedback and help them to find and correct errors. Many students will be able to correct their own computational errors, especially if students are working in pairs or small groups. When students are unable to fix their errors due to more serious misconceptions, the teacher can step in to help develop understanding. This helps the teacher use their time efficiently and focus on students facing challenges.
I've recently seen one math activity used in a number of classrooms in a variety of forms. I'll call this activity a "question chain" although I've seen it referred to using lots of different names. This activity starts with a set of questions and associated answers. Students start by solving one of the questions. The answer to this first question leads the student to the next question. This process is repeated until the student arrives back at the starting question. The answers form a "solution bank." If the student can't find their answer, they know that they've made a mistake and need to find and correct their error. Below are three different ways that I've seen this activity implemented in classrooms.
Questions on Cards
Questions Posted on the Wall
Questions on a Worksheet
Selecting a Method
During a recent professional development session with math teachers, we tried this activity using all three methods. Participants were split into three groups and each group was given a different method. All three versions of the activity included the same ten questions (see the files below).
After completing the activity we had a discussion to compare the three methods. All of them took about the same amount of preparation and could be quickly created using questions from a textbook or other problem bank. How would students record their work in each method (on paper, mini-whiteboard, etc.)? How would the teacher assess students work in each method? Would each method work better individually, in pairs or in small groups? How might this activity be used in a combined grade classroom? Which method might be most culturally relevant for your students and how does your knowledge of your students inform your selection of a method? Which method is the most engaging for your students? We had a very productive and rich discussion.
Have you used this type of activity in your classroom? Another variation of this method is the "I have/ who has?" oral classroom activity. Have you used a different variation of any of these methods in your class? Do you have a favourite method? Why is it your favourite?
Activities that let students get immediate feedback on how their are doing are extremely beneficial. Activities that allow students to self-check their own work allow for this immediate feedback and correction. These types of activities can allow the teacher to focus their time with students who are having conceptual misunderstandings and not get bogged down helping students find and correct computational errors. While students are engaged in self-checking activities, the teacher can also be working with small groups of students on mini-lessons or conversations/conferences. Below are a few of my favourite activities and routines that allow for students to check their own work:
Team Post-Its - I recently saw this activity described in a post by Julie Morgan. This activity is very easy to set up and does not require much front loaded time to create. The teacher posts a list of questions for small groups of students to work on. These might even be questions from the textbook. Each group solves the question, writes their answer on a sticky note and posts it on the whiteboard. As other groups complete the questions, they can compare their answers to those from other groups to see if they agree. If they don't agree, they double check their work. I would suggest that each group of students starts with a different question.
Add ‘Em Up - In this activity, students do a set of problems, either on their own or as a group. These problems typically have numerical answers. The answers to the set of problems are added up and compared to the sum provided. If the sum is not the same, then the student knows that one or more of the problems in the set was done incorrectly and works to find the error. I first saw this activity described in a blog post from Kate Nowak. I later saw a blog post from Amy Gruen describing a simple and quick way to do this same activity that I used occasionally. There are many descriptions of how to organize this activity including one in a detailed blog post from Sara VanDerWerf.
Row Game - I also first saw this activity described in a blog post from Kate Nowak. Typically, a row game is a worksheet of problems organized in two columns. The worksheet is completed by a pair of students, one doing the problems in column A and the other doing the problems in column B. The problems in each row have the same answer so if the students' answers don't match, they can work together to check their solutions to find the error. To make row games a bit easier to create, you can create an additional column with the sum of the solutions from column A and B (similar to the Add 'Em Up activity from above). This allows you to use any two problems and not have to create two problems with the same solution. Kate Nowak has a shared google folder with a large selection of crowd-sourced row games.
Added 03Oct017 - I recently saw a great idea from Heidi Neufeld. She asked students who finished quickly to make a new row for the row game and create two different problems with the same answer.
Mathematical Circuit Training / Around the World / Star Chain / Question Stack - There are lots of different names for and variations of this activity. The essential part is that there is a series of problems and the answer for each problem leads you to the next question to ask. The answer to the final question leads you back to the starting question. This activity can be organized as a simple worksheet, a stack of cards to turn over, a set of cards to chain together or questions posted on signs around the classroom or hallway. If you make a mistake, you won't be able to find the next question and you know to try again. This can be done individually or in small groups.
Added 26Sep2017 - Thanks Alicia!
Invisible Ink - The description of this activity is from a blog post from David Petro. Students solve a set of problems on a card. When ready, they can check their solutions using an answer card. This card has the correct answers written with "invisible" ink that can only be seen by shining a small UV light on it. Once the student has solve the questions correctly, they move on to the next card containing more complex questions. David says, "Students really seem to like this style of activity as they feel empowered to move from card to card when they are ready and the added feature of checking the answers with the UV pen gives a sense of novelty."
If you know of any other self-checking activities that I've missed, please let me know and I'll add them here.
I was introduced to row games while reading Kate Nowak's blog several years ago. A row game is an activity for a pair of students to work on together. Problems are organized in two columns. The first student completes all of the problems in column A and the second student completes all of the problems in column B. The questions in each column are different but the answers are the same. Students collaborate to verify that their answers match. If they do, they move on to the next question. If the answers do not match, the students work together to find out where the error was made and how to fix it. This allows students to have immediate feedback on their work. It also generates great discussions between students as they check each other's work. Another benefit is that students can correct each other's computational errors and the teacher's time can be focused on helping students with more serious comprehension errors.
Row Game Links
There are a couple of great resources for row games online. Kate Nowak has a shared Google drive folder packed with mathematical row games for a variety of grade levels and topics. Another row game collection is available on John Scammell's Orchestrated Experiences for High School Math website.
Nova Scotia Mathematics 10 Cumulative Review Row Game
Below is a row game that I created as a cumulative review for Mathematics 10. I created about half of the questions myself and appropriated the rest from row games created by Kate Nowak, John Scammell, and David McGuinness.