Our parents have changed their perspective, but have we changed ours?

One part of my job is occasionally leading parent workshops. I think they are so important, but they give me so much anxiety. I will spend several hours planning for a 1 hour workshop. I will rehearse what I am going to say over and over, because I want it to be perfect. At least that’s what I tell myself. But in truth, what I really want is to fill the time to avoid parent questions. Because I hold this assumption that parents are angry we teach math this way; I assume our parent community thinks more traditional methods, quick repetitious pace, and rote instruction is what is best.  
And that’s implicit bias. I was adopting a single story of what these parents are like because it has been fed to be over and over. Author, Chimamanda Ngozi Adichie warns us of accepting a single story in this brilliant Ted Talk. What’s more, this single story and Chinese education is wrong. In fact, according to this Quartz article, in typical Chinese math classes there is more time spent on collective learning and less time using an individualistic approach. The whole class does not move on until the entire class has the concept. In a sense, collaboration and support of one another is nurtured. 
 At the most recent ES math parent coffee, my co-presenters and I did our best to be inclusive of the parent community. Many of the slides were written in English and Mandarin, they were able to collaborate, we provided materials for them to take in both English and Chinese, and we used several visuals to accompany our slides. We created space and access for our parents to not just sit and get but engage. And  the 40 parents that attended were beautiful examples of learners. They explored the mathematics problems, listened to one another, collaborated, had a laugh, and took risks. Not once in the oral or written feedback did I hear anything about parents wishing we didn’t teach math this way, nor was there anger or frustration that math class looks different now. The sentiment was appreciation for the opportunity to learn this way.  
Now I don’t want to sugarcoat it, I’ve been at ISB for 5 years now and I know that the parent feedback about our approaches to teaching math has not always been this positive. But, if our parents have shown us that they are willing to change, why are we still holding these negative biases about what we think they think? Have we been as willing to grow, change, and shift as our larger parent community?  
So. I hope next time you feel that discomfort when a colleague says something about our parent population, or a group of students, or a cultural group, in seriousness or in jest, that you’ll remember that people can grow and change. And I hope it encourages you to say something. 
 We have a responsibility as educators to move our community towards cultural proficiency. I know it can make things awkward. I know it can make people uncomfortable. I know it takes bravery. Brené Brown, a prominent research storyteller says, “courage is contagious. Every time we choose courage, we make everyone around us a little better and the world a little braver.” Seems like something worth doing, doesn’t it? 

My Ongoing, Messy, Roundabout Journey Toward Cultural Proficiency

Do you notice yourself remembering the names of the white kids more easily than the names of the Asian kids?” 
This was asked of me last year by a close friend and colleague. And it hit me like a ton of bricks. Because as I thought about which students I acknowledged by name in the hallway, who I would ask teachers about, who I took time to build rapport with I was unconsciously investing more time in the white kids. Research says that we do tend to have a natural affinity for  people that we see as like us. In fact, an article published by Phi Delta Kappan “recent studies have found that children as young as three months old can racially categorize people” (Hagerman, M.A., 2019). 
AND I am someone that sees myself as an advocate for marginalized groups. I speak out, often to the point where it makes my family shift in their seats, about injustices in the world. I recognize that as a white, heterosexual, cisgender, English speaking woman, I have a huge amount of privilege. I feel a duty to use my privilege to support others and dismantle systems of traditional power in the world. And yet, I still hold implicit bias and look for what’s familiar and comfortable. 
An article published this summer by actor N’Jameh Camara talks about why some names are more memorable than others. She speaks honestly about how when people don’t use her name and instead use a “generic substitute,” she notices. She challenges us to think that names are not “hard” or “difficult to say” but rather “unpracticed.” I love that. Perhaps my favorite quote is, “but as a person who was taught to respect and say Tchaikovsky, Brecht, Chekhov, Stanislavski, and Hammerstein, I know my name can be learned too. What matters most is that we see ourselves as people whose vulnerability and mistake-making hold the potential to bring us closer” (Camara, N., 2019).  
Fortunately, recognizing that we hold implicit bias is a crucial first step in doing something about it. Founder of the C6 Biliteracy Framework and honorary ISB Dragon, Dr. José Medina, shares the Cultural Proficiency Continuum in his trainings and I find myself referring to it constantly. It has supported me in recognizing when we are being culturally destructive. This continuum has given me the language and tools to reflect and speak up when I hear things that are not inclusive and supporting of our community. 

Original source of continuum: Lindsey, R.B., Robbins, K.N., and Terrell, R. D.  (2009). Cultural Proficiency A Manual for School Leaders. Examples and quotes original.  

As a coach at ISB, I get the honor to work with and learn from the incredible educators here. I am so fortunate to see the high-quality teaching and care teachers share with students. I am all in when it comes to helping others who I coach, I care deeply about them as people and care completely about nudging them to where they want to grow. But as coach, as Elena Aguilar says in her article, “I have to keep the faces of all the children who [teachers] are responsible for, whose lives [teachers] affect, in my symbolic peripheral vision, equally in focus and present and part of the conversation. I am accountable to those children” (Aguilar, E., 2014). Coaching or collaborating without a focus of creating equity and access for our students is a missed opportunity we cannot afford to pass up.  
My journey towards cultural proficiency is not over. I still slip up, or occasionally bite my lip when I hear something that marginalizes others. But I am also committed to improving. If you have books, research, ideas, people you follow, tips and suggestions, or just want to talk about this with someone, I would love to learn. 

Aguilar, E. (2014). Why we must all Be Coaches for Equity. Education Week. http://blogs.edweek.org/teachers/coaching_teachers/2014/12/why_we_must_all_be_coaches_for.html 
Camara, N. (2019). Names That Are Unfamiliar to you Aren’t “Hard,” They’re “Unpracticed”. Teen Vogue. https://www.teenvogue.com/story/names-that-are-unfamiliar-to-you-arent-hard-theyre-unpracticed?fbclid=IwAR0rwGC_Xxs59fUSKgBErE2vl9tA2ASVmmwHfqmNwdULnJm17cs0Qup3k_A 
Hagerman, M.A. (2019). Conversations with Kids about Race. Phi Delta Kappan. https://www.kappanonline.org/conversations-children-race-childhood-racism-hagerman/ 
Lindsey, R.B., Robbins, K.N., and Terrell, R. D.  (2009). Cultural Proficiency A Manual for School Leaders. 

Rethinking Mathematics Fluency

A common challenge I hear from teachers and parents is that their students do not know their basic math facts, meaning their addition, subtraction, multiplication, and division facts using numbers 0-9. What generally follows are questions of how to support their students with building this mathematical fluency. It’s widely accepted and known among teachers that the drill and kill, rote memorization of facts is not the best way for students to develop automaticity (quick recall) and in fact “the lowest achieving students worldwide [on the PISA tests] were those who used a memorization strategy” (Boaler, 2015). However, we recognize that mastering basic math facts is critical to building a strong foundation to conquer more complex mathematics and that “the past decade [of math instruction] has produced a generation of students who are procedurally competent but cannot think their way out of a box” (Boaler, 2015). This leaves many teachers scratching their heads at what to do and what is the best support to offer parents.  
One common misconception is that because fluency development is now taught differently that it no longer carries as much importance as it previously did. There is also the misconception that with an inquiry based and conceptual understanding approach that fluency will be developed naturally. In reality, fluency must be developed in tandem and partnership with conceptual understanding and “without that skill our students will view even simple math tasks as daunting” (O’Connell, p. 2). Our goal for students regarding math fluency should not just be memorization but automaticity, understanding, and connection making. In order for our students to really develop mathematical fluency with basic facts understanding and memorization must partner.  
A case for understanding 
We cannot expect students to internalize and commit math facts to memory without providing the opportunities to develop understanding first. Compare this to when we are teaching children to read. Asking students to memorize a string of words (such as book in favorite and sat I my chair a read) is much more difficult than when the words are put into context (I sat in my favorite chair and read a book) (O’Connell). Robbing students of the chance to develop understanding in context takes away opportunities for students to be problem solvers and utilize patterns. Teaching students facts with no context lacks authenticity, often leads to confusion and mix-ups, and does not allow students to develop reasonableness about their answers. 
A case for memorization 
On the other hand, any teacher would recognize the importance of students being able to recognize and recall math facts. There are many benefits to students committing facts to memory. When facts are automatic it allows the brain to grapple with more complex components of the task like patterns, fractions, or spatial reasoning. It allows students to answer problems more efficiently, and positions students to solve every day mental math tasks.  
Before we expect students to master and recall facts they must have a solid footing in number sense. First, students should have opportunities to investigate facts through discussions, games, and using concrete materials. Then, students should explore strategies that support their understanding. Finally, students should have targeted and strategic practice with memorization. Below I share some suggestions and routines for how to incorporate more authentic practice that builds students math fluency.  
Tips to develop math fluency appropriately 

  • Consider varying the order with which students learn multiplication math facts. Teaching facts in sequential order takes away the opportunities for additional sense making. A suggested progression is 2, 10, 5, 1, 0, 3, 4, 6, 9, 8, and 7 because the progressions build on pattern making and base ten. 
  • Fluency activities should be short in duration (5-10 minutes at a time) and frequent (a few times a week). 
  • Fluency activities should be varied to maintain engagement. 
  • Speed games and timed drills before students have developed fluency can block working memory and prevents students from accessing facts they know and can lead to develop math anxiety (Boaler, 2015). 
  • Be wary of how Engage New York (ENY) defines fluency. ENY claims that a memorization of facts allows students to successfully complete more complex tasks. This is not supported by research and ignores the importance of number sense (Boaler, 2015).  
  • Progress towards automaticity and fluency should be monitored and shared with students through conferences, data, and goal setting (O’Connell, 2011). 
  • When students are finding answers using manipulatives and visuals always record the corresponding equation.  
  • Ask questions when looking at equations
    • What do the numbers represent?  
    • Can you break apart the factors to help you find the answer? 
    • How is this different from…? 
  • Use several different models (area model, arrays, double number lines, set models, etc.) to show the same fact. 
  • When applicable connect math facts to literature. The Doorbell Rang, Two of Everything, If you Hopped like a Frog, Cloudy with a Chance of Meatballs, Snowmen at Night, Snowflake Bentley, Thunder Cake, and One Hundred Angry Ants all provide points of integration. 

Routines and Lesson ideas to develop math fluency appropriately 

  • Number Talks 
  • Skip counting routines 
  • Quick Images with Dot Cards, ten frames, arrays, dominoes, real life objects (Shumay, 2018) 
  • Encourage students to write their own story contexts to demonstrate their understanding of math facts 
  • Today’s Number routine (Shumay, 2018) 
  • Ways to Make a Number routine (Shumay, 2018) 
  • Ten Frames Routines (Shumay, 2011) 

Grade Level Specific Resources 
Building Conceptual Understanding and Fluency Through Games in Kindergarten 
Building Conceptual Understanding and Fluency Through Games in Grade 1 
Building Conceptual Understanding and Fluency Through Games in Grade 2 
Building Conceptual Understanding and Fluency Through Games in Grade 3 
Building Conceptual Understanding and Fluency Through Games in Grade 4 
Building Conceptual Understanding and Fluency Through Games in Grade 5 
References and additional reading 
Boaler, Jo (2015). Fluency without Fear. 
Boaler, Jo (2015). Memorizers are the lowest achievers and other Common Core math surprises. 
Boaler, Jo (2016). Speed and Time Pressure Blocks Working Memory. 
O’Connell, Susan, and SanGiovanni, John (2011). Mastering the Basic Math Facts in Multiplication and Division.  
Parrish, Sherry (2010). Number Talks. 
Shumay, Jessica (2011). Number Sense Routines Building Numerical Literacy Every Day in Grades K-3. 
Shumay, Jessica (2018). Number Sense Routines Building Mathematical Understanding Every Day in Grades 3-5. 
Van de Walle, John A. et al. (2018). Teaching Student-Centered Mathematics K-2.  
Van de Walle, John A. et al. (2018). Teaching Student-Centered Mathematics 3-5 

Getting real about Learning Objectives

I feel the need to be honest with you, ISB. I am a content and language objective convert.  I will admit that when I was first told that we would write daily content and language objectives for math I was compliant but skeptical and quietly resistant.  I looked for shortcuts, kept the same generic objectives up for days, hardly shared them with students, and kept them designated to a hard to see corner in my room. I was beginning the journey, but hardly moving.    
And, since we’re being completely honest with each other, even after my initial training with the brilliant Dr. José Medina, I still wasn’t convinced. I was inspired and enthusiastic about supporting emergent bilinguals in my classroom, but I did not see how being more intentional about objectives would positively impact student learning.  I know I am not alone in my struggle with objectives. How do we manage the seeming polarity between inquiry and creativity with COLOs? How do we balance wonder and curiosity with routines?  
My short answer? Write better objectives.  
Recently, I read this article from Lustre Education that reminded me of my initial feelings about objectives. The author posits that objectives, or learning targets, rob students of the opportunity to explore concepts and inhibit deeper learning. As the SIOP instructional coach here, I have heard the same argument made among our faculty. But I will assert that if we are not writing, posting, and reviewing our content and language objectives, we are doing our students a disservice.   

  • COLOs are proven to have a positive impact on student learning. Let’s get down to the numbers. For reference anything above an effect size of 0.40 is considered significant.*
    • COLOs enhance teacher’s clarity.  Teacher clarity has a 0.75 effect size.   
    • COLOs promote classroom discussion. Classroom discussion has a 0.82 effect size.
    • COLOs encourage self-verbalization and self-questioning. Self-verbalization and self-questions has a 0.64 effect size.  
    • COLOs are an example of student-centered teaching. Student-centered teaching has a 0.54 effect size.  
    • COLOs provide goals and outcomes for students. Goals has a 0.50 effect size.  
    • COLOs communicate learning and language expectations. Expectations has a 0.43 effect size.  
    • By contrast, teacher subject matter knowledge has an effect size of 0.09. 
  • COLOs are a differentiation tool. In posting accurate content and language objectives they give language learners and student who receive learning support the permission to focus and excel at one thing at a time.  
  • COLOs allow teachers to be more student-driven and student-focused. Because COLOs are written for the student, a teacher is thinking through what students need to learn and how they will show they learned it. It is not about what the teacher will do, but what evidence the teacher will gain from student performance.   
  • COLOs build community. Specifically, language objectives highlight the opportunity for students to communicate and intentionally listen to one another. They foster an environment where students learn from each other and from the teacher as well as promote risk-taking, learning from mistakes, patience, and empathy.  
  • COLOs promote authentic interaction. When students are communicating during a lesson with specific COLOs they already have a frame of how to interact. They know the skill they will be communicating about (content) and the aspect of language acquisition they will be practicing. 
  • COLOS provide a springboard to new thinking. For our students that are fluent English speakers or already have a solid understanding of the content, COLOs can be the jumping off point to ask themselves “and what else can I pursue within this topic?” For example, if the content objective is “I am learning to multiply fractions less than 1 whole,” curiosity might be peaked to explore areas like how patterns apply to numbers greater than 1 whole, how patterns connect to decimals, negative numbers.   
  • COLOs can help manage off task behavior. COLOs bring our students (and us) back to the intention of the lesson when we’ve gotten too far off track. We’ve all been in the situation where one student has a connection and it opens a whole parade of stories. Being able to say, “How does your connection support our study of point of view?” or “I’d love to hear about roller coasters when we’re walking to lunch, but for now let’s get back to learning about blends” validates the students while refocusing the group.

How to craft better content and language objectives  

  • Create them with your students. I saw a beautiful example in a grade 1 classroom. The teacher began by saying “Today we’re going to keep thinking about adding numbers and showing our thinking. What might our content objective be?” After listening to students, he paraphrased and wrote on the board. Students immediately saw their thinking validated. Then he asked, “How will we show we can add using more than one strategy?” which led students to suggest they could write their thinking clearly or they could talk to the teacher about what they did. COLOs done.  
  • Replace the word ‘learning’ to ‘inquiring’ or ‘exploring’. Feeling locked in or uninspired by “I am learning to…”? Perhaps try “I am inquiring into…”, “I am exploring…”, or “I am puzzling about…” as a way to open up thinking.  
  • Commit to introducing  them with students. One of the most powerful ways I grew in crafting purposeful objectives was when I became intentional about sharing them with students. I knew that if I shared the objective at the beginning of the lesson and saw puzzled looks, scratched heads, heard “huh?”, or had to further explain what they meant, then I had not crafted a student-centered objective.   
  • Commit to reviewing them with students. Sometimes our lessons go in different directions than we anticipate. Sometimes this is awesome, exciting, and enriching, but sometimes it is unproductive learning and thinking. In reviewing the objectives it reminds us and our students of the goals that still need to be achieved.  
  • Use action verbs from Blooms Taxonomy to specify what students are doing. The more intentional we can be about our language the more likely students are to reach the desired learning outcome. Do you want them to measure? Design? Generalize? Tell them in the objective.  
  • Use specific action words to specify reading, writing, listening, and speaking objectives.
    • Reading: locate, skim, find, discover, distinguish 
    • Writing: question, explain, list, revise, justify, summarize, record  
    • Listening: distinguish, categorize, follow directions, choose  
    • Speaking: debate, define, express, predict, restate, share, tell 
  • Use cultural objectives to connect skills to the real world and the hidden curriculum. Ultimately, we want our students to be kind, good hearted, accepting people. This goes beyond the discrete skills and knowledge that are emphasized through content and language objectives. Cultural objectives provide the opportunity for students to make connections to their community, their lives, and the world around them. Cultural objectives are golden opportunities to touch on learning dispositions such as curiosity, problem solving, and critical thinking. Something like “I can be curious about patterns in numbers” or “I can recognize patterns to help me solve problems in the real world.” 

To end with one more bit of honesty, I can confidently say that Content and Language Objectives, when utilized correctly can positively impact all the students in your classroom. 
*All data is taken from John Hattie et al.’s book Visible Learning for Mathematics (2017)  

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