16 thoughts on “Making Meaning: Oral Language and Context Matter”
Jana,
Thanks for the I sights on language and context. Excited to hear what it is like for students with IEPs. I know this is old but number talks are great ways to get kids to explain themselves. They have to use formal language to explain the process of solving.
My favorite research study on language acquisition in content classes is by Gibbons:
Gibbons, P. (2003). Mediating language learning: Teacher interactions with ESL students in a
content-based classroom. TESOL Quarterly, 37(2), 247-273.
She shows how the contexts allow students who are language learners to use indexical language that has lower demands (e.g., “that” while pointing), while being scaffolded over time into the formal academic language (e.g. “the vertex of the triangle.”) Let me know if you need a copy.
The other essential reading about oral language in the classroom in my opinion:
Cazden, C. (2001). Classroom discourse: The language of teaching and learning (2nd edition). Portsmouth, NH: Heinemann.
Unlocking English Learners’ Potential (Strategies for Making Content Accessible) by Fenner and Snyder has some great strategies for using scaffolding, teaching academic language and background knowledge and structuring formative assessments with students learning English as new language.
That the observed progress in your class that persisted and learned to speak mathematics was 2 years of growth in a single year is no surprise, but wonderful to hear of. My experience working with a ‘remedial’ math skills program, in which most of the students were also in a remedial reading/writing program,for 13 years at a university assured me that problems in interesting local context (context that those students relate to and care about) is critical for most people who are not already in love with mathematics, or in the midst of falling in love with it. However, in the instances where the students were loath to speak with each other as they worked, progress was always much slower and considerably less learning was finally achieved.
This corresponded to my experience with teaching advanced high school mathematics in an inner city school where a focus on interesting and significant context was my biggest concern.
The only successful strategy for getting oral communication to happen where it was not already enthusiastically adopted was to sit down with one or two ‘mediocre’ students and engage in conversation about the problem with them, leading them to express their interest in it and give ideas about it. All that in the sight and hearing of the rest of the class. I am deeply interested in hearing of other methods.
The way I worked with teachers who taught the university’s math skills courses (referred to above) was to give them the same problems that I wanted them to use with students. As they worked in their groups, we stopped to talk about what was happening in their minds and what we all hoped would happen for students. There, I am guilty of having focused mainly on the way context supports deep understanding and not also focusing on how talking about the problem and about the solving of it supports the reasoning, the learning, and retention of the math concepts learned in the activity. Which may be why I sometimes found that the teachers made no particular effort to get their students to talk, even though they put them into small groups for the activities. Many of the students came from cultures where a version of English was the lingua franca but standard English was often a little way outside their experience, except as the language of schooling.
Now I am working with teachers where the children speak Kriol everywhere except school. The teachers speak Kriol, too, but they teach and provide activities in standard English. Thank you for helping me think about this situation.
Thank you for posting your thoughts.
I have started to look at the vocabulary in the problems and what the words mean and how is that meaning related to the math. Listening to the students talk and discovering their meanings and using that insight to guide your teaching will help fill in the foundation that they are missing due to language or misconceptions.
I have been married to my husband for 45 years. He is Dutch and English is his second language. We still have issues with misinterpreting words due to the words having different meanings or nuances.
Keep the dialogue going and you have pointed out how we need to make math more visual and be more cognizant of the vocabulary we use.
I love the visual of the iceberg – I also think about how the tip of the iceberg represents only what we see – with ELL students or students with disabilities we often “see” a lack of engagement, not contributing to discussions, needing long wait times, etc. But once we stop and take time to “look” below what we see AND interpret from our lack of understanding, we learn that students are thinking deeply about the problem rather than what we interpret as disengagement or lack of understanding. It may take a student longer to process so we have to be ok with waiting longer for their response and not rob them of their opportunity to share. It may take a student longer to formulate their thinking in their own language and then translate that to English. Do we provide different ways students can express their ideas – manipulatives, whiteboards, colored pens, movement, etc. that gives each child an access point? As you share about language and the challenge when English is not your first language (or Dutch), I imagine the incredible energy that ELL students must put in each day to make sense of new learning in many different content areas, all the while having to make sense in their own language and then translate it to English. I can’t imagine the times of confusion, misunderstanding, and getting lost an ELL student must experience that we don’t “see” but is happening below the surface. What questions can we engage in with students to get to know their culture and what might cause confusion. Last night we put on a community evening for families and their preschool children to learn about early literacy. Our focus was on phonological awareness particularly with rhyming words. One family who attended was from China. As we spent time talking with the family, they shared that rhyming words do not exist in the Chinese language – so this was a completing new idea. Who would have known?
My last thought in response to Maurine’s comment – I also feel that Mathematically Productive Instructional Routines such as Number Talks, My Favorite Know, Noticing and Wondering, etc. have been wonderful instructional practices that support ELL and SWD in expressing their ideas and building their confidence in sharing those ideas.
Great post. I agree. I remember visiting my husband’s family and they were all speaking Dutch or the native language which I can’t spell and being so lost and tired by the end of the day. I also had trouble staying awake listening to these long conversations with no visual clue as to what was being said.
The iceberg graphic is blowing my mind and reminding me of other famous authors who support this idea…
1) Grace Kelemanik, Amy Lucenta & Susan Janssen Creighton in their book Routines for Reasoning. (https://www.heinemann.com/products/e07815.aspx). They claim that the 8 Math Practices (U.S. Standards), or in general, the teaching of reasoning opens doors for students with special needs; it does not create barriers.
2) Keith Devlin of Standford. At the NCSM national conference he stated that “symbols are a wonderful way of using mathematics and a horrible way of learning it.”
I really want to share this post of yours. Let us know when that will be available.
Hi Chris and Jana,
I agree with Chris that we would like to share your post with other math teachers.
Let us know when we can.
PS. Chris, it is great to see a friend involved in this project.
For me the iceberg metaphor captures some but not all of what I would want to say about the relationship between formal notations and informal representations. It captures the idea that any formal notation compresses a lot of ways of thinking and seeing into one compact form. There are two comments I would make about this compact form.
First, the formal notation by itself is meaningless without the abstract idea that it represents. That abstract idea is more than just the sum of the things below the water line. It is really a new thing, and it’s the abstract idea that is the true goal of the progression through informal and preformal representations.
Second, the iceberg metaphor does not capture the dynamic relationship between the concrete representations beneath the water line and the abstract idea above it. Once students have abstracted the notion of, say, 3/4, from the various representations, they can return to those representations and see them in a new light. The mass of the iceberg disappears because what appeared to be a cumbersome collection of different representations becomes organized into a single crystalline object revealed in all its multicolored complexity.
Phil Daro described this interplay between abstract and concrete in a beautiful way in an email to me tonight, talking about Mathematical Practice Standard #2 (Reason abstractly and quantitatively). “MP2 is not getting the attention and clarity it deserves . . . as a younger cousin of modeling . . . abstraction can make thinking easier. Embezzling abstraction within a concrete situation, concrete>abstract>concrete, enables reasoning with simple, sleek abstractions without the cumbersome mass of concrete. The abstract reasoning could be as simple as calculation or it could be solving equations or it could be grow up into formulating mathematical models. “
Thank you for your comment. It makes me wonder new things, and I love that.
I appreciate the connection to MP2. Ideally, the abstract arises because students have a need for it. I see this happen for my sixth graders as they learn how to reason about the area of plane figures. Most of them begin with counting squares and parts of squares and then counting becomes impossible, or at least not enjoyable, so they need another way to think about it. This reminds me of Dan Meyer’s phrase ‘having a headache.’ (He uses it in the context of three-act tasks, but I like the metaphor.) In this way a level of abstraction — seeing a triangle as half of a parallelogram, for example — is ‘aspirin for the headache.’ In time, thinking about parallelograms itself becomes cumbersome and a formula can become the ‘aspirin for the new headache.’
I love Phil Daro’s use of the word embezzling. Too often teachers want the learning process to progress neatly from concrete to abstract when really it is a back and forth interplay with students returning to the concrete time and again as they acquire new tools. If I understand you, when you say the abstract idea ‘is really a new thing’ that means that it itself becomes real to the student as something that they can work with regardless of the presence of context. If we think about it that way, the model falls apart a bit because there is something very important outside the iceberg.
I think that idea of the abstract being really a new thing is something we often miss in our instruction. It is a leap and an act of creation that does not happen for everyone at the same time and in the same way. I wonder, what can we look for and listen for in our students to know this has happened?
I too have seen and related to the iceberg model. I also really appreciate Bill’s comments about when, through understanding, it “compacts” into something completely different, something more fully conceptualized and ready to be used productively elsewhere. Jana, I will be thinking much about your question of what can we look and listen for in our students to know this has happened.
Your phrase of “my race to the top of the iceberg” struck me as it captured well the pressure teachers commonly express to “wrap up” or “clean up” the thinking of the class at some point in the lesson or unit.
I found myself in this situation recently during a probability unit in my math for elementary education class. With the end of the quarter looming and our time running short, I found myself wanting to lead them out of muddle they were in. I decided this was a sure sign I needed to give them another day to muddle, and the understanding they developed by continuing to defend their different perspectives was much more valuable than my “tidying up” would have been. This could, I think, be an example of allowing them to make sense of and “compact” the various representations versus me dragging them to the top of the iceberg.
Upon reflection, I’m convinced that I felt this pressure especially in this unit because my own thinking in probability is less flexible than my thinking in other content areas. Another argument for ongoing content learning experiences for educators.
I agree with Maurine Bailey that number talks can provide an avenue for students to communicate about their thinking in a non-threatening way and build their own mathematical confidence as individuals. Another valuable gain results when teachers have to stop communicating for students, and listen to learn how their students are thinking in a particular number talk situation. While students build precise language skills, teachers are challenged to clearly represent how a student sees the math so that others in the learning community understand, and more importantly, the student speaking feels understood.
Having learned about Number Talks from Ruth Parker, I also learned not to assume that silence implies a lack of understanding. There are a few students who process internally and do not want to speak in front of others. Not using the language doesn’t mean you can’t communicate, if given a safe environment or alternative.
Hello, As an ELL teacher my thoughts resonate with supporting students to be able to communicate their ideas and confusions. I have found that using levelled language frames (sentence frames designed for different levels of English proficiency support students to be able to begin to communicate. I also see that when language learners can observe proficient students communicating, especially with visuals, about their thinking, number talks for example, this offers great modelling for language learners. Then, next step is to encourage these students to try to verbalize their own ideas. Drawing is a great tool. Often ELL students can understand more than they can verbalize. It is our job to scaffold this understanding though providing tools to aid their ability to verbalize their ideas to level the playing field and include the ELL learners in the content discussions. Levelled langauage frames help to support language learners to deepen their verbal ability to communicate their ideas.
Our school has also recently begun to use a program called Depth and Complexity, in which certain icons are used for cultivating deeper discussion or to generate ideas. This program can be used in any content area. I wanted to also share a book I have used a great deal by Jeff Zwiers, Susan O’Hara, and Robert Prichard called: Common Core Standards in a Diverse Classroom; Essential Practices for Developing Academic Language and Disciplinary Literacy.
Hello, As an ELL teacher my thoughts resonate with supporting students to be able to communicate their ideas and confusions. I have found that using levelled language frames (sentence frames designed for different levels of English proficiency support students to be able to begin to communicate. I also see that when language learners can observe proficient students communicating, especially with visuals, about their thinking, number talks for example, this offers great modelling for language learners. Then, next step is to encourage these students to try to verbalize their own ideas. Drawing is a great tool. Often ELL students can understand more than they can verbalize. It is our job to scaffold this understanding though providing tools to aid their ability to verbalize their ideas to level the playing field and include the ELL learners in the content discussions. Levelled langauage frames help to support language learners to deepen their verbal ability to communicate their ideas.
Our school has also recently begun to use a program called Depth and Complexity, in which certain icons are used for cultivating deeper discussion or to generate ideas. This program can be used in any content area.
Wow – you have some really powerful comments here! I especially appreciated both the iceberg model and the notion that it was necessary to ‘muddle’ around a bit – sortof like you walking around trying to describe your pathway/experiences in Dutch – I have had the same experience in Italy with my Italian – but coming to something firm that makes sense is so satisfying! As I have seen it this past year in the 4th grade classroom with the ELL students – allowing them to ‘muddle’, draw pictures, try to explain their thinking in multiple languages, and come to an understanding – watching that light bulb go on is so rewarding. But as Debbie pointed out, we have to be patient, in spite of that need to ‘wrap things up’.
One thought I had while reading towards the bottom was something I heard years ago (I wish I could remember where!) but have quoted ever since, “Math, done right, most often can be MESSY!”
Jana,
Thanks for the I sights on language and context. Excited to hear what it is like for students with IEPs. I know this is old but number talks are great ways to get kids to explain themselves. They have to use formal language to explain the process of solving.
My favorite research study on language acquisition in content classes is by Gibbons:
Gibbons, P. (2003). Mediating language learning: Teacher interactions with ESL students in a
content-based classroom. TESOL Quarterly, 37(2), 247-273.
She shows how the contexts allow students who are language learners to use indexical language that has lower demands (e.g., “that” while pointing), while being scaffolded over time into the formal academic language (e.g. “the vertex of the triangle.”) Let me know if you need a copy.
The other essential reading about oral language in the classroom in my opinion:
Cazden, C. (2001). Classroom discourse: The language of teaching and learning (2nd edition). Portsmouth, NH: Heinemann.
Hope this helps!
Unlocking English Learners’ Potential (Strategies for Making Content Accessible) by Fenner and Snyder has some great strategies for using scaffolding, teaching academic language and background knowledge and structuring formative assessments with students learning English as new language.
That the observed progress in your class that persisted and learned to speak mathematics was 2 years of growth in a single year is no surprise, but wonderful to hear of. My experience working with a ‘remedial’ math skills program, in which most of the students were also in a remedial reading/writing program,for 13 years at a university assured me that problems in interesting local context (context that those students relate to and care about) is critical for most people who are not already in love with mathematics, or in the midst of falling in love with it. However, in the instances where the students were loath to speak with each other as they worked, progress was always much slower and considerably less learning was finally achieved.
This corresponded to my experience with teaching advanced high school mathematics in an inner city school where a focus on interesting and significant context was my biggest concern.
The only successful strategy for getting oral communication to happen where it was not already enthusiastically adopted was to sit down with one or two ‘mediocre’ students and engage in conversation about the problem with them, leading them to express their interest in it and give ideas about it. All that in the sight and hearing of the rest of the class. I am deeply interested in hearing of other methods.
The way I worked with teachers who taught the university’s math skills courses (referred to above) was to give them the same problems that I wanted them to use with students. As they worked in their groups, we stopped to talk about what was happening in their minds and what we all hoped would happen for students. There, I am guilty of having focused mainly on the way context supports deep understanding and not also focusing on how talking about the problem and about the solving of it supports the reasoning, the learning, and retention of the math concepts learned in the activity. Which may be why I sometimes found that the teachers made no particular effort to get their students to talk, even though they put them into small groups for the activities. Many of the students came from cultures where a version of English was the lingua franca but standard English was often a little way outside their experience, except as the language of schooling.
Now I am working with teachers where the children speak Kriol everywhere except school. The teachers speak Kriol, too, but they teach and provide activities in standard English. Thank you for helping me think about this situation.
Thank you for posting your thoughts.
I have started to look at the vocabulary in the problems and what the words mean and how is that meaning related to the math. Listening to the students talk and discovering their meanings and using that insight to guide your teaching will help fill in the foundation that they are missing due to language or misconceptions.
I have been married to my husband for 45 years. He is Dutch and English is his second language. We still have issues with misinterpreting words due to the words having different meanings or nuances.
Keep the dialogue going and you have pointed out how we need to make math more visual and be more cognizant of the vocabulary we use.
Jana,
I love the visual of the iceberg – I also think about how the tip of the iceberg represents only what we see – with ELL students or students with disabilities we often “see” a lack of engagement, not contributing to discussions, needing long wait times, etc. But once we stop and take time to “look” below what we see AND interpret from our lack of understanding, we learn that students are thinking deeply about the problem rather than what we interpret as disengagement or lack of understanding. It may take a student longer to process so we have to be ok with waiting longer for their response and not rob them of their opportunity to share. It may take a student longer to formulate their thinking in their own language and then translate that to English. Do we provide different ways students can express their ideas – manipulatives, whiteboards, colored pens, movement, etc. that gives each child an access point? As you share about language and the challenge when English is not your first language (or Dutch), I imagine the incredible energy that ELL students must put in each day to make sense of new learning in many different content areas, all the while having to make sense in their own language and then translate it to English. I can’t imagine the times of confusion, misunderstanding, and getting lost an ELL student must experience that we don’t “see” but is happening below the surface. What questions can we engage in with students to get to know their culture and what might cause confusion. Last night we put on a community evening for families and their preschool children to learn about early literacy. Our focus was on phonological awareness particularly with rhyming words. One family who attended was from China. As we spent time talking with the family, they shared that rhyming words do not exist in the Chinese language – so this was a completing new idea. Who would have known?
My last thought in response to Maurine’s comment – I also feel that Mathematically Productive Instructional Routines such as Number Talks, My Favorite Know, Noticing and Wondering, etc. have been wonderful instructional practices that support ELL and SWD in expressing their ideas and building their confidence in sharing those ideas.
Great post. I agree. I remember visiting my husband’s family and they were all speaking Dutch or the native language which I can’t spell and being so lost and tired by the end of the day. I also had trouble staying awake listening to these long conversations with no visual clue as to what was being said.
The iceberg graphic is blowing my mind and reminding me of other famous authors who support this idea…
1) Grace Kelemanik, Amy Lucenta & Susan Janssen Creighton in their book Routines for Reasoning. (https://www.heinemann.com/products/e07815.aspx). They claim that the 8 Math Practices (U.S. Standards), or in general, the teaching of reasoning opens doors for students with special needs; it does not create barriers.
2) Keith Devlin of Standford. At the NCSM national conference he stated that “symbols are a wonderful way of using mathematics and a horrible way of learning it.”
I really want to share this post of yours. Let us know when that will be available.
Hi Chris and Jana,
I agree with Chris that we would like to share your post with other math teachers.
Let us know when we can.
PS. Chris, it is great to see a friend involved in this project.
Jana,
For me the iceberg metaphor captures some but not all of what I would want to say about the relationship between formal notations and informal representations. It captures the idea that any formal notation compresses a lot of ways of thinking and seeing into one compact form. There are two comments I would make about this compact form.
First, the formal notation by itself is meaningless without the abstract idea that it represents. That abstract idea is more than just the sum of the things below the water line. It is really a new thing, and it’s the abstract idea that is the true goal of the progression through informal and preformal representations.
Second, the iceberg metaphor does not capture the dynamic relationship between the concrete representations beneath the water line and the abstract idea above it. Once students have abstracted the notion of, say, 3/4, from the various representations, they can return to those representations and see them in a new light. The mass of the iceberg disappears because what appeared to be a cumbersome collection of different representations becomes organized into a single crystalline object revealed in all its multicolored complexity.
Phil Daro described this interplay between abstract and concrete in a beautiful way in an email to me tonight, talking about Mathematical Practice Standard #2 (Reason abstractly and quantitatively). “MP2 is not getting the attention and clarity it deserves . . . as a younger cousin of modeling . . . abstraction can make thinking easier. Embezzling abstraction within a concrete situation, concrete>abstract>concrete, enables reasoning with simple, sleek abstractions without the cumbersome mass of concrete. The abstract reasoning could be as simple as calculation or it could be solving equations or it could be grow up into formulating mathematical models. “
Thank you for your comment. It makes me wonder new things, and I love that.
I appreciate the connection to MP2. Ideally, the abstract arises because students have a need for it. I see this happen for my sixth graders as they learn how to reason about the area of plane figures. Most of them begin with counting squares and parts of squares and then counting becomes impossible, or at least not enjoyable, so they need another way to think about it. This reminds me of Dan Meyer’s phrase ‘having a headache.’ (He uses it in the context of three-act tasks, but I like the metaphor.) In this way a level of abstraction — seeing a triangle as half of a parallelogram, for example — is ‘aspirin for the headache.’ In time, thinking about parallelograms itself becomes cumbersome and a formula can become the ‘aspirin for the new headache.’
I love Phil Daro’s use of the word embezzling. Too often teachers want the learning process to progress neatly from concrete to abstract when really it is a back and forth interplay with students returning to the concrete time and again as they acquire new tools. If I understand you, when you say the abstract idea ‘is really a new thing’ that means that it itself becomes real to the student as something that they can work with regardless of the presence of context. If we think about it that way, the model falls apart a bit because there is something very important outside the iceberg.
I think that idea of the abstract being really a new thing is something we often miss in our instruction. It is a leap and an act of creation that does not happen for everyone at the same time and in the same way. I wonder, what can we look for and listen for in our students to know this has happened?
I too have seen and related to the iceberg model. I also really appreciate Bill’s comments about when, through understanding, it “compacts” into something completely different, something more fully conceptualized and ready to be used productively elsewhere. Jana, I will be thinking much about your question of what can we look and listen for in our students to know this has happened.
Your phrase of “my race to the top of the iceberg” struck me as it captured well the pressure teachers commonly express to “wrap up” or “clean up” the thinking of the class at some point in the lesson or unit.
I found myself in this situation recently during a probability unit in my math for elementary education class. With the end of the quarter looming and our time running short, I found myself wanting to lead them out of muddle they were in. I decided this was a sure sign I needed to give them another day to muddle, and the understanding they developed by continuing to defend their different perspectives was much more valuable than my “tidying up” would have been. This could, I think, be an example of allowing them to make sense of and “compact” the various representations versus me dragging them to the top of the iceberg.
Upon reflection, I’m convinced that I felt this pressure especially in this unit because my own thinking in probability is less flexible than my thinking in other content areas. Another argument for ongoing content learning experiences for educators.
I agree with Maurine Bailey that number talks can provide an avenue for students to communicate about their thinking in a non-threatening way and build their own mathematical confidence as individuals. Another valuable gain results when teachers have to stop communicating for students, and listen to learn how their students are thinking in a particular number talk situation. While students build precise language skills, teachers are challenged to clearly represent how a student sees the math so that others in the learning community understand, and more importantly, the student speaking feels understood.
Having learned about Number Talks from Ruth Parker, I also learned not to assume that silence implies a lack of understanding. There are a few students who process internally and do not want to speak in front of others. Not using the language doesn’t mean you can’t communicate, if given a safe environment or alternative.
Hello, As an ELL teacher my thoughts resonate with supporting students to be able to communicate their ideas and confusions. I have found that using levelled language frames (sentence frames designed for different levels of English proficiency support students to be able to begin to communicate. I also see that when language learners can observe proficient students communicating, especially with visuals, about their thinking, number talks for example, this offers great modelling for language learners. Then, next step is to encourage these students to try to verbalize their own ideas. Drawing is a great tool. Often ELL students can understand more than they can verbalize. It is our job to scaffold this understanding though providing tools to aid their ability to verbalize their ideas to level the playing field and include the ELL learners in the content discussions. Levelled langauage frames help to support language learners to deepen their verbal ability to communicate their ideas.
Our school has also recently begun to use a program called Depth and Complexity, in which certain icons are used for cultivating deeper discussion or to generate ideas. This program can be used in any content area. I wanted to also share a book I have used a great deal by Jeff Zwiers, Susan O’Hara, and Robert Prichard called: Common Core Standards in a Diverse Classroom; Essential Practices for Developing Academic Language and Disciplinary Literacy.
Hello, As an ELL teacher my thoughts resonate with supporting students to be able to communicate their ideas and confusions. I have found that using levelled language frames (sentence frames designed for different levels of English proficiency support students to be able to begin to communicate. I also see that when language learners can observe proficient students communicating, especially with visuals, about their thinking, number talks for example, this offers great modelling for language learners. Then, next step is to encourage these students to try to verbalize their own ideas. Drawing is a great tool. Often ELL students can understand more than they can verbalize. It is our job to scaffold this understanding though providing tools to aid their ability to verbalize their ideas to level the playing field and include the ELL learners in the content discussions. Levelled langauage frames help to support language learners to deepen their verbal ability to communicate their ideas.
Our school has also recently begun to use a program called Depth and Complexity, in which certain icons are used for cultivating deeper discussion or to generate ideas. This program can be used in any content area.
Wow – you have some really powerful comments here! I especially appreciated both the iceberg model and the notion that it was necessary to ‘muddle’ around a bit – sortof like you walking around trying to describe your pathway/experiences in Dutch – I have had the same experience in Italy with my Italian – but coming to something firm that makes sense is so satisfying! As I have seen it this past year in the 4th grade classroom with the ELL students – allowing them to ‘muddle’, draw pictures, try to explain their thinking in multiple languages, and come to an understanding – watching that light bulb go on is so rewarding. But as Debbie pointed out, we have to be patient, in spite of that need to ‘wrap things up’.
One thought I had while reading towards the bottom was something I heard years ago (I wish I could remember where!) but have quoted ever since, “Math, done right, most often can be MESSY!”