(This is the last post in a two-part series. You can see Part One here.)
The new question-of-the-week is:
What is the single most effective instructional strategy you have used to teach math?
In Part One, Cindy Garcia, Danielle Ngo, Patrick Brown, and Andrea Clark shared their favorite math instructional strategies.
Today, Joy Hamm, Lauren Nifong, and Jim Ewing 鈥渨rap up鈥� this series.
Word-Problem Summaries
Joy Hamm has taught 11 years in a variety of English-language settings, ranging from kindergarten to adult learners. The last few years working with middle and high school Newcomers and completing her M.Ed. in TESOL have fostered stronger advocacy in her district and beyond:
Beware of teaching math vocabulary out of context! For example, teaching students that 鈥渓ess than鈥� means 鈥渟ubtract鈥� gets muddy as students advance through more challenging word problems (鈥�3 less than x鈥� does NOT mean 鈥�3-x鈥�).
A more effective instructional strategy for word problems is utilizing math-talk summaries/paraphrases. Start by modeling some examples and then move into paired practice. To include newcomers, pair them with a more advanced EL (English learner) who speaks the same home language or use the Google Translate app for peer interaction. All students have the capacity to summarize and think aloud regardless of the language they use to communicate their understanding of the word problem.
In pairs, one student (the stronger reader) reads aloud the word problem. Example: 鈥�Mario is hired to take 572 glass jars to a flower shop. The florist (shop worker) will pay Mario a $100 flat fee (pay that doesn鈥檛 change), plus $2 for every jar that is delivered safely. However, Mario must pay the florist $5 each for any jars that are lost or broken. If two jars are lost, four jars are broken, and the rest are delivered safely, how much should Mario be paid?
The second student listens and creates a summary of the word problem (in any language since the focus is comprehension, not English).
Example: 鈥淢ario is moving lots of glass jars. He gets $100, and that won鈥檛 change, but he can make more money if he doesn鈥檛 break any jars. Also, Mario will lose money if he breaks or loses jars. So, we need to figure out how much money Mario makes after delivering, breaking, and losing some jars.鈥�
Next, both students use the summary to figure out which math operations and steps are needed to solve the problem. Example of math talk: 鈥淟ost and broken jars means subtract $, delivered safely means add $. Wow, it鈥檚 going to take a long time to add up all of the jars safely delivered with the extra $2 for each jar; we could multiply the number of jars delivered by $2 to go faster. So, are we going to start by multiplying or by adding and subtracting?...鈥�
Summarized word problems avoid common student pitfalls such as highlighting the visible numbers and coming up with an answer such as 572 jars-2 jars-4 jars- $5 + $100 +$2=663 jars or money?? Thus, student word-problem summaries help ELs comprehend the story line in the word problem before attempting to figure out the proper operations needed.
Guided Math
Lauren Nifong is an instructional coach in Greenville, S.C. She holds a bachelor鈥檚 degree in elementary education, a master鈥檚 degree in administration and supervision, and is currently a member of South Carolina ASCD鈥檚 2020 Class of Emerging Leaders. You can connect with Lauren at @Lnifong0320 on Twitter:
As teachers, we always strive to meet the needs of every student. That sentence alone can seem daunting to many. How do we truly meet the needs of EVERY child? Our classroom is filled with a myriad of ability levels, complexities, strengths, and weaknesses. Teachers work countless hours developing lesson plans and engaging activities for their classroom, but even the most 鈥渟how worthy鈥� lessons can fail to be effective if teachers are not focused on differentiation.
Throughout my years as a math teacher, I quickly realized that it was going to take more than 鈥淚 Do, We Do, You Do鈥� to truly target the individual needs of the students within my room. After attending several professional developments, I stumbled across the Guided Math approach. I participated in a book study with Laney Sammon鈥檚 book: Guided Math: A Framework for Mathematics Instruction. We talk about our 鈥渁-ha鈥� moments with students, but this was most certainly my 鈥渁-ha鈥� moment as an educator. What impressed me the most about this practice was the intentionality of individualized instruction. By using meaningful formative assessments, teachers are able to analyze data to determine the exact levels of all students, group them according to their greatest needs, and then implement small-group lessons that truly targeted those needs in order for students to build the foundational skills needed to be successful in their grade-level content.
In addition to individualized instruction, the Guided Math model puts emphasis on building true conceptual understanding of math before moving on to procedural learning. Remember those pesky math manipulatives? Hands-on learning is essential to deepening the understanding of difficult content, but many manipulatives end up halfway across the room before you even have them distributed to all the students.
Small-group instruction allows students to use math manipulatives in a controlled environment with immediate feedback from the teacher. Talk about a lifesaver for classroom management! This easy management aspect is appealing, but the true beauty of using small groups is their fluidity. With Guided Reading, students may stay in a certain group for several weeks at a time based on their reading level. With math, things can get a little more complicated. A student who is proficient in algebra may struggle with geometry. With math groups, you can move students (using your collected data) and vary groups based on their targeted need for that specific content. This process ensures that students鈥� individual needs are met in the most intentional and effective way possible.
So, what do you do with students who are not meeting with you in a small group but left to work independently or in collaborative pairs/groups? Effective management is imperative to the success of the entire workshop model. Laney Sammons published another resource called Guided Math Workshop. She details how to successfully manage a classroom where multiple levels of learning happen simultaneously. Holding students accountable is crucial. The teacher needs to be intentional about student pairing, and students must be required to record and submit written (or electronic) work so that the teacher can check in frequently.
Unlike a small group, which is grouped homogeneously, collaborative pairs/groups who are not working directly with the classroom teacher need to be based on heterogeneous grouping. This allows for students to pull on the strengths of each other to successfully complete a task. And whether you require students to record their work in a math journal to be the subject of random checks by the teacher or have students submit an exit ticket from group/independent work on a daily basis, it is important for the students to know their work has a purpose and it was created intentionally to aid in their learning process.
As educators, we often say phrases like, 鈥淚f it works, don鈥檛 fix it鈥� or 鈥淒on鈥檛 recreate the wheel,鈥� but ask yourself these questions: Is it really working? Are you truly meeting the individual, unique needs of every child that walks through your door? If there was any hesitation in your answers, then I highly recommend taking a closer look at the Guided Math model.
Turn & Talk
Jim Ewing is an assistant professor and author of the book Jim provides motivating, relevant, and strategy-driven workshops for teachers that get results. To learn more about his workshops and book, go to EwingLearning.com:
Ineffective Strategy: 鈥淩aise your hand when you know the answer.鈥�
This strategy is inequitable. If we ask this question, the same few will answer our questions over and over. The goal for teachers should be to develop students鈥� conceptual development and academic language. If only some students are answering our questions, then only some are learning.
This practice is especially unfair for English-learners. Empathize how ELs may feel solving content in a second language. Imagine the following scenario in 鈥淪panglish.鈥�
What is 鈥渃inco mas ocho?鈥� Raise your hand when you know the answer.
How would you solve this problem if you don鈥檛 speak Spanish well? At my workshops, teachers often share their thinking like this:
Step 1: I translate cinco to five
Step 2: I translate ocho to eight.
Step 3: I know 鈥渕as鈥� means 鈥渕ore鈥� but why is he asking us 鈥渇ive more eight?鈥�
Step 4: If I say 鈥渕ore鈥� the numbers should be getting bigger, so he is probably asking us to add or to multiply.
Step 5: I am not sure, but it might be addition.
Step 6: Five plus eight is 13.
Step 7: Ten is diez; 11 is once; 12 is doce; 13 is trece.
Step 8: I think the answer is trece.
Now tell me. If you were a student and your teacher had asked you to raise your hand when you knew the answer, would you? Probably not. By the time you went through all the steps, another student who speaks Spanish fluently would have already called out the answer. After a while, you might shut down and thus not develop mathematical understanding or learn essential academic vocabulary.
When we ask students to raise their hands when they know the answer, it only rewards the few students that work quickly. This practice is especially unfair for ELs because it takes time to translate content into another language. Instead of asking our students to work quickly in math, we should encourage our students to persevere. When we focus on persevering to solve problems, each student can be successful.
Effective Strategy: 鈥淭urn and talk to your neighbor鈥�
Alternatively, if teachers ask students to turn and talk to their neighbor, each student has an opportunity to engage in mathematics and develop academic language. Applying the example above, it would be much less intimidating to share with a partner rather than with the whole class. While the students are sharing, the teacher can listen in on conversations. Instead of calling on the same fast student who raises his/her hand, the teacher can choose who should share with the whole class.
For example, the teacher can listen to a shy student and validate the student鈥檚 answer. Then the teacher could say, 鈥淣ora, I like your answer. The class would benefit from hearing it. Would you like to share how you solved the problem?鈥� If the student is hesitant, Nora might share with the help of a partner. If she is still hesitant, with permission, the teacher could ask Nora if she could share Nora鈥檚 thinking with the class. Then the class could discuss Nora鈥檚 reasoning, which may raise her social status and make her more engaged in learning the math concepts in the future.
If we shift from asking students to share their thinking with a partner instead of raising their hands when they know the answers, each student can prosper. After all, the focus of mathematics should not be to praise the few who work fast. When we focus on strategies that value speed, some students win and some students lose. Instead, we should encourage all students to persevere to solve problems. Let鈥檚 focus on strategies like talking to a neighbor to encourage each student to be successful in math.
Thanks to Joy, Lauren, and Jim for their contributions!
Please feel free to leave a comment with your reactions to the topic or directly to anything that has been said in this post.
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