Five ways to phrase questions to engage all students

Inspired by five weekends in August ... weekend edition ... sharing five fives on Saturday this month to celebrate #MTBoSBlaugust!

How can you phrase questions to engage all students in participating in class?  Here are five ideas ... 



Be specific about waiting:  "Don't raise your hand; I want everyone to have time to think about this!  Be ready to explain your process in 57 seconds ... setting the timer now for think time!"   

Choose a few students to share their work:  "Take a minute to visualize this problem.  Can you write or sketch a possible [solution, example, counterexample]?  As I walk around the room, I'm going to select 3 students to share their work with the class."

Encourage more than one correct answer:  "Create an example to support this [problem, statement, scenario] and write it down.  In a minute we will share examples to see how many ways the [problem, statement, scenario] can be supported."

Check individual work:  "Put the next step on your whiteboard; be ready to explain why this step is necessary. I'll take a tour of the room to see your work; I may ask you to share your reasoning."  

Encourage sharing:  "Stop and jot down your thoughts on this problem.  In a minute you are going to share your ideas with your partner."

Resources for Habit 6 Question for Understanding

Habit 6 in Teaching Numeracy: 9 Critical Habits to Ignite Mathematical Thinking matches our school's initiative well.  One focus last year was critical thinking.  To analyze our effectiveness in addressing critical thinking we focused on questioning.

Pearse and Walton stress the importance of preplanned high level thinking questions.  Most of us have heard of research that says in most classes teachers ask mostly low level questions.  It takes specific planning to be sure to use worthwhile questions.  Rarely will they just happen.

Resources that I have used to help with questioning strategies include these books.

I wrote about these books in a previous blog post.  In that blog I also note a helpful resource by Ontario Ministry of Education, an excellent article entitled, "Asking Effective Questions," which has question stems for planning high level questions for various instructional purposes.  These are similar to what Pearse and Walton have included in their book.

As Pearse and Walton point out, keep such a list of questions or question stems handy when planning is helpful in designing optimal questions.  In addition to keeping lists handy, using a template for planning discussion around a problem or question is useful.  The book Intentional Talk has such templates.  Those templates are free right now on the Stenhouse Publishers website.  You can also preview the entire book for free there as well.  Currently there is a slow math chat about this book on Twitter!  Check out the hashtag #intenttalk or this blog post on the summer long chat!

One area I want to work on is making sure all students are participating in the thinking when I ask questions.  I've been reviewing the book, Total Participation Techniques.  Some of those participation techniques include think, pair, share; quick writes; whiteboard responses; hold-up cards, four corners, and more. Since we will have iPads this year, I am looking for free apps that we can use easily as participation techniques that will add to our learning.  One strategy I saw this week, is having students respond to a prompt, capturing a screen shot, and adding to it Padlet.  I can envision students working out or illustrating their work in educreations or desmos, capturing it and sharing.  Then we can easily talk more about individual students' strategies.  Hopefully by sharing more student responses we can generate more student questions!

If you haven't read Teaching Numeracy: 9 Critical Habits to Ignite Mathematical Thinking, check it out.  Yes, it has an elementary focus but the habits apply to all of schooling!

Questions to Think Through While Planning

I've been thinking about lesson planning.  I've never written down the questions that passed through my mind as I planned. Now I'm trying to recreate those.

1. What do I want students to be able to do at the end of the lesson? vocabulary? skill? application? depth of understanding?


2. How will the vocabulary, skill or application in this lesson be tested?


3. What is the rationale for this lesson? 


4. What connections can I help students make to real world application? How can I help students visualize this math? 


5. What came before? What will come after? How can I link this lesson with the others?


6. What connections do I want students to make to previous work? What might those connections look like?
   


7. How will I know students "get" this lesson? What questions will I ask? In what format will I frame those questions?


8. At this point I often check the MTBoS search engine for blogs about this lesson. Is there a way to get at this lesson without direct explicit instruction? If so, how shall I set up students' learning? What notes will students need?  What do those notes look like? What practice will students need? What active learning strategy fits this lesson best? What differentiation is needed so that all students can participate?


9. What problems will I use? Do they need to be scaffolded ... basic to difficult? What student errors can I anticipate? How can I use those anticipated errors to support students?
   


10. What does the pacing look like in this lesson? Are there different activities? If so, what is the sequence of events? How will I handle transitions?


11. What materials do I need to prepare? What does the room arrangement look like? If students are in groups - how will I organize those?


12. What might plan B look like if any part of this lesson fails?

What questions do you think about as you plan lessons? Please share!

#MTBoSBlaugust Planning for Questioning & Resources

Questions and questioning are at the heart of rich math dialogue.

Questioning “to-do” or “not-to-do” list

1. Ask meaty questions … not one-word answer questions.
2. Ask open-ended questions!
3. Don’t announce questions as easy or difficult.
4. Give students time to think about your question.
5. Ask a question, give time to think … then call on a student.
6. Don’t answer your own questions.
7. Don’t repeat a student’s answer.  Instead ask another student to explain if clarification is needed.
8. Ask the follow-up question … “Why?” or “How do you know” or “Can you elaborate?”
9. Use your poker face during discourse – don’t give your thoughts away with facial expressions.
10. Invite student questions as much as possible!
11. Use questioning as a teaching tool in place of the standard lecture.
12. Don’t use questions as a disciplinary tool.

In Teaching Numeracy: 9 Critical Habits to Ignite Mathematical Thinking, Pearse and Walton stress the importance of preplanned high level thinking questions.  Most of us have heard of research that says in most classes teachers ask mostly low level questions.  It takes specific planning to be sure to use worthwhile questions.  Rarely will they just happen.


I have found a few resources to use to help me in preparing good questions.

1.  I love the NRICH Enriching Mathematics site!  It is many excellent resources from articles to challenging problems!  This article, Developing a Classroom Culture That Supports a Problem-solving Approach to Mathematics, caught my attention.  The author offers ways to think about the questions you ask, how to group them, and possible question stems.  Check it out!

2.  Want to use Socratic Questioning?  This blog post explains six categories of Socratic questions and provides question stems for each category!  Excellent resource!

3.  At the Ontario Ministry of Education, there is an excellent article entitled, "Asking Effective Questions."  In the article there are eight tips for asking effective questions.  Additionally there are many, many questions or question stems providing an amazing framework for asking good questions. Keeping such a list of questions or question stems handy when planning is helpful in designing optimal questions.  In addition to keeping lists handy, using a template for planning discussion around a problem or question is useful.  The book Intentional Talk has such templates.  Those templates are free right now on the Stenhouse Publishers website.  You can also preview the entire book for free there as well. 




4.  Another book to have on your shelf is this book by Schuster and Anderson.  The book is set up by strands in math. The questions are open-ended and challenging.  For example:  "Carla and Fiona are having a mathematical debate about the equation y = 1/2 x + 3.  Carla thinks that every time y changes by one, x changes by 2.  Fiona thinks that every time y changes by one-half, x changes by one.  What do you think?"






5.  I like yet another book for its ideas on differentiating.  It is also organized in strands.  For each topic, the authors, Small and Lin, provide ideas for open questions and 2 parallel questions at different levels.  One example that caught my eye is:  "Another function is a lot like the given function.  What might it be?  Option 1:  y = 3x^2 + 4  Option 2:  y = 3^x.  Follow up questions are provided:  What happens to your function when x gets big?  When x is quite small?  What kinds of things might you change but still have a similar function?  What would you choose not to change?





Do you have resources to help you plan deep, thought-provoking questions?  Share resources in the comments!

#MTBoSBlaugust Phrasing to Engage All Learners In the Math Classroom

How can you phrase questions to engage all students in participating in class?  Here are five ideas ... 

#MTBoSChallenge Week 4 ... reflecting on the first days

Reflecting on our first two weeks ...

Trying to ask better questions ...

Day 1:

• "How does this equation relate to the problem situation?"  
• "Are all the points generated by the regression equation valid for the problem situation?  Explain why."
• Why is the domain/range for the equation different from the problem situation?  Would that always be true?

Day 2

• When might this description of a relationship be discrete?  When might it be continuous?

Day 3

• How are these parent functions similar?  How are they different?

Day 4

• Let's don't mention your solutions right now.  Describe the processes you are using to solve the puzzle ... 

Students were feeling uneasy on the first day ... but each day I see more students growing more confident in sharing their thoughts.  We've also had the opportunity to celebrate incorrect responses, opportunities to point out that it's OK to make mistakes, it's in the mistakes that we learn the most!

#70Days Students Asking Questions!

Day 7

Devotional thought from Practice Resurrection:  If we calculate the nature of the world by what we can manage or explain, we end up living in a very small world.

This is the context in which Peterson begins his exposition of Ephesians 1:3 - 14.  In the Greek Ephesians 1:3 - 14 is one long sentence, about 200 words, and noted as "one of the most splendidly Jewish passages of praise and prayer in the New Testament ... a prayer of blessing to the one God for his mighty acts in creation and redemption."

Today I am meditating on Peterson's paraphrase of the first few verses of this "song of praise" ... How blessed is God! And what a blessing he is! He’s the Father of our Master, Jesus Christ, and takes us to the high places of blessing in him. Long before he laid down earth’s foundations, he had us in mind, had settled on us as the focus of his love, to be made whole and holy by his love. Long, long ago he decided to adopt us into his family through Jesus Christ. (What pleasure he took in planning this!) He wanted us to enter into the celebration of his lavish gift-giving by the hand of his beloved Son. (from The Message, Eph. 1:3 - 6)

This morning I have been re-reading the chat we had last night about getting students to ask questions.  Here is a LINK to the article that we read.  And here is a COPY of our chat!

Last year, on day 1, we started with our first "I Notice, I Wonder" activity.  I had made a chart of the seven functions we would study.  Students wrote down their noticing and wondering.  You can read about the activity HERE.

This year I am thinking about extending that activity into asking questions.  The chart could be my QFocus. Students could work in small groups around large whiteboards.  That way we can easily share our thoughts. I envision this activity occurring on Day 2 of our school year - when we are introducing the parent functions.  It will be interesting to see what questions students develop and how we can apply their questions in our unit.  One of the ideas discussed last night in our chat was inviting students to choose a question or two to answer for homework.  That way students have ownership - of the questions and the homework.  Hopefully that will be a win-win for them! I'm wondering also if I can include one or more of their own questions on our assessments during the unit of study!

Just now I was thinking about how we could hang our charts around the room - the noticing, wondering, questions ... but if we use the group whiteboards it's harder to save their work.  Yes - I do take pictures but printing those out chart size isn't an option for me.  We need to capture a summary of our work on "anchor charts" that we can refer to throughout the unit!

Before the summer is over, I plan to study more about students asking questions.  At Right Question Institute (Twitter #QFT) there are free resources.  My reading/thinking/planning pile is growing!

Last ... join us in our Twitter Chats ... we read one article a week and discuss them at 8 pm central time on Wednesday evenings!  See Read Chat Reflect Learn and #EduRead on Twitter!

#70Days: Getting reading for #EduRead!

Devotional phrase today from Peterson's Practice Resurrection: " The diversity of gifts adds up to a unity of function."  (I happen to love the mathematical word choices!)

"Each Christian participates in his or her own specific way in the context and conditions of his or her own life circumstances, but none of us do it on our own or under our own power."

We have been gifted to do the work and doing the work leads to maturity ... ours and those in our sphere of influence.

"But to each one of us grace has been given as Christ apportioned it. So Christ himself gave ... to equip his people for works of service, so that the body of Christ may be built up until we all reach unity in the faith and in the knowledge of the Son of God and become mature, attaining to the whole measure of the fullness of Christ." (Ephesians 4:7-13)

Then I saw this tweet this morning and I couldn't help but relate it to my devotional time ... in giving gifts to His people Christ sets us up to be in positions to succeed!  And we are grateful!

I can only imagine the overflowing warmth this teacher must have felt from this student's high praise!

Today is Wednesday - the day for on of my favorite Tweet Chats ... #EduRead.  Tonight we are discussing an article from the Harvard Education Letter, Volume 27, Number 5, published September/October 2011.  The title is "Teaching Students to Ask Their Own Questions."  I'm interested in this chat because I see too many bright, energetic students waiting to be spoonfed instead of pursuing their own curiosities in math!

I'm sharing my notes and questions from the article ...

This is my experience as well:

• Or, as one teacher put it: “I would often ask my students, ‘Do you have any questions,’ but, of course, I didn’t get much back from them.”

These are significant outcomes:

• In the classroom, teachers have seen how the same process manages to develop students’ divergent (brainstorming), convergent (categorizing and prioritizing), and metacognitive (reflective) thinking abilities in a very short period of time.
• When teachers deploy the QFT in their classes, they notice three important changes in classroom culture and practices. Teachers tell us that using the QFT consistently increases participation in group and peer learning processes, improves classroom management, and enhances their efforts to address inequities in education.

The process is flexible:

• Teachers can use the QFT at different points: to introduce students to a new unit, to assess students’ knowledge to see what they need to understand better, and even to conclude a unit to see how students can, with new knowledge, set a fresh learning agenda for themselves.

Questions I am pondering in advance of our discussion tonight!

• How does this idea fit with other routines I already use in your classroom? For example, I used “I notice; I wonder" fairly consistently in the fall ... then let that practice slip away. How might I strengthen the process?
• What might work well as a QFocus in my Algebra 2 classes?

One thing that captures my attention from this article is that in the process the students sort their questions as open or closed, try to improve their questions, and then rank order their questions (top three!) This alone is such a great thinking routine!

Looking forward to our discussion tonight ... #EduRead at 8 pm. Also check out the Read, Chat, Reflect blog! Share an article or two that we need to discuss this summer!
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Time now for a bit of list making ... we leave for a week at the beach on Saturday.  I am sure I have some "stuff" to do!

Questions and Dialogue

At the beginning of our unit on systems of equations we discussed the question, What is a solution?
We returned to the question as I introduced solving linear inequalities and systems of linear inequalities.  Students participated readily ... less pause than the first time around ...

What is a solution?

Student A: anything that satisfies the equation ...
Me:  could someone add to that thought?
Student B:  it's the numbers that solve the equation ...
Me:  Hmmmm, I don't think we can use the root word in the definition ... any other thoughts?
Student C:  it fits in the equation
Me:  OK ... it satisfies, it solves, it fits ... any other thought?
Student D:  it makes the equation true
Me:  Yes ... to all of the above!
Me:  Now, if I give you an equation with 2 variables, how might you represent the solution visually?
Student E:  could you restate that question?
Me:  (I write on the board) y = 2x + 3; How might I represent the solution to this equation visually?
Student F:  (2, 7)
Me:  OK, that point is true.  How else might I represent the solution visually?
(pause)
Me:  OK ... are there other solutions besides (2, 7)?
Several students:  yes ... many of them ... infinite number
Me:  Yes!  So how might I represent those infinite solutions visually?
Student G:  a line
Me:  Yes!  So how or why does a line represent the infinite solutions to that equation?
Student H:  a line continues in both directions forever
Student I:  a line is made of infinite number of points
Me:  Yes!

We then extended our conversation to include inequalities ... talking about why we shade and what that tells us.

I want to get better at asking questions ... I want to ask better questions.  I also want to develop strong math discourse in our class!

These are the "essential" questions suggested by our district curriculum document:

1. Describe the solution to a system of equations with 3 variables.
2. How do you determine the variables for a system of equations?
3. How do you write a system of equations from information given in a problem situation?
4. How do you know if your solution to a system of equations is reasonable?
5. How do you connect the solution to a system of equations to the context of a problem 
6. situation?
7. How do you decide which method to use to solve a particular system of equations?
8. How do you solve systems with more than two variables?

These questions hit the surface and skim across the topic.  I want something deeper, richer for my students.

MTBoS: Help with Systems unit??

Hey math friends ... looking for some inspiration ...

Given:  Algebra 2 (advanced students)
... note ... they studied systems of equations in Algebra 1 (2 years ago)

Constraints:

1. 4  90 minute class periods
2. Must teach solve by graphing, solve by substitution, solve by elimination, and word problems
3. Those 4 topics are usually the heading for each of the four days
4. The solve by graphing day will include inequalities
5. The word problems must include some wind and river current problems
6. We teach solving by matrices in a separate unit

I have typical lesson plans ... and plenty of typical practice problems.

One of my goals this year is to use better problems, better questions, time for noticing/wondering, opportunities for developing students' curiosity.

Do you have suggestions for an opening problem for the unit?  Or better yet, an opening problem for each day?

Beth
Check out my 180 blog!

Blogosphere ... Good Ideas Round 3

As I have been reading around the blogosphere, I am in awe of the many excellent ideas shared among educators!

Here are 3 ideas that caught my eye!

Our school is fortunate to have a 1:1 initiative for 9th and 10th grades.  (Last year only freshmen were issued laptops).  I am always on the lookout for meaningful ways to embed technology in my algebra classes.  I ran across Education Rethink: Fifteen Paperless Math Strategies.  I notice that several of the strategies involve a blog and/or a shared document.  I've already committed to learning how to use Google products more effectively - thinking the shared document will work.  One more note at this blog ... this team of two offer their visuals for free ... which may be helpful as I create materials for class!

Mary Dooms writes a poignant post about students and curiosity in response to Dan Meyer's post on The Unengageables. She says, "Students are curious. We just have to give ourselves permission to allow them to pose questions and wonder."  Mary goes on to talk about how we use the summer to recalibrate; this resonated with me!  Mary mentions the Annenberg series and Fostering Algebraic Thinking.  My stack of books is growing and the time I'm spending reading them is shrinking!  Her post inspires me to keep at the work of developing good problems - worthy of students' curiosity!  Check out her 7th grade textbook revision problem!

To follow up on developing good problems, a third site I found interesting is Inquiry maths! As we discuss textbook revisions at #MakeOverMonday and read professional books, developing rich worthwhile mathematical discourse is essential! I'm looking at the inquiries suggested for algebra and considering how I might use these to stimulate creative and analytical thinking. The author at Inquiry Maths says "Inquiry is built on inquisitiveness and curiosity. And for those to be articulated, students need to learn how to ask questions. When students inquire into their own questions, levels of motivation, engagement and confidence rise. Students become self-starters who take responsibility for their own learning. Importantly, they lose the fear of giving the wrong answer because they control the question under consideration."

So much to think about ... so little time ... even in the summertime!   The math blogosphere is an amazing source for professional development!

eliciting student responses

Chapter 4, "Eliciting Evidence of Learner's Achievement" in Wiliam's Embedded Formative Assessment is all about ways to figure out if students have learned what has been taught.

The chapter includes very practical discussions of how to elicit responses.  I have been guilty of calling on the students who raise their hands knowing full well that the others are quite willing to let those few answer all the questions!  One suggestion in the book is that students should only raise their hands if they have a question.  The teacher should have a plan for calling on students randomly in discussion.  I used a random name generator and the students loved it.  But because it was online, it tied up my computer/projector ... made it difficult to flip back and forth if I was displaying questions electronically.  I purchased Popsicle sticks last year but never wrote students' names on them.  I think that I need to put them in place for the coming year.  But I might try this "card-o-matic" idea ... names on index cards, same name on more than one card, cards on a ring ... looks easy!

To gather input from all students, I plan to make a simple A, B, C, D card for students to keep in their binders.  To add variety, I'll use technology as well.  Clickers are great if they are available.  We can use Socrative since our 9th graders are being issued laptops.

Students love to use their phones.  I saw the Spanish teacher's students talking on phones near the end of school.  I asked her what they were doing.  She uses Google Voice to capture student dialogue.  Students dial her Google Voice number and "leave a message!"   I want to explore this tool for sure ... would love for students to verbally explain their work to me.

Besides the practice "how-to" capture students' responses, the author discussed the kinds of questions to ask and how the right question can tell us so much about a student's thinking.  One example had two equations:  3a = 24 and a + b = 16.  Students were asked to solve them.  Students were puzzled, said it couldn't be done.  It confused them that in this set of equations a and b both equal eight.  It's so true that so many of our examples are carefully contrived, that it is difficult for students to overcome the hidden patterns that we teach.

Another example, Simplify (if possible):  2a + 5b, at first glance seemed unusual.  The author purports that this example is fair and worthy.  If a student can be tempted to simplify that expression, then the teacher needs to know that before moving on.

This chapter challenges me to consider the questions I'm asking in class and the methods I use to collect student responses.

How do you engage all learners in responding to discussion?
What are your best questions?

Questions and more questions!

Questions and questioning are at the heart of rich math dialogue.  We are in our first week of school and I realize that I need to work on my questioning skills to tap into the strengths of my diverse students.

I have found a few resources to use to help me in preparing worthwhile questions.

1.  At the Ontario Ministry of Education, there is an excellent article entitled, "Asking Effective Questions."  In the article there are eight tips for asking effective questions.  But then there are many, many questions or question stems providing an amazing framework for asking good questions.

2.  I also ran across this book by Schuster and Anderson.  The book is set up by strands in math.  Even though I teach algebra, I find this book useful in developing questions to help my ninth graders make sense of the prerequisite math that they still struggle with.  The questions are open-ended and challenging.  For example:  "Carla and Fiona are having a mathematical debate about the equation y = 1/2 x + 3.  Carla thinks that every time y changes by one, x changes by 2.  Fiona thinks that every time y changes by one-half, x changes by one.  What do you think?"

3.  One other book I ran across provides ideas for differentiating.  It is also organized in strands.  For each topic, the authors, Small and Lin, provide ideas for open questions and 2 parallel questions at different levels.  One example that caught my eye is:  "Another function is a lot like the given function.  What might it be?  Option 1:  y = 3x^2 + 4  Option 2:  y = 3^x.  Follow up questions are provided:  What happens to your function when x gets big?  When x is quite small?  What kinds of things might you change but still have a similar function?  What would you choose not to change?

I'm on the prowl for other great resources for developing strong questioning skills.  Send me a note if you know of others!