What can we do for HS students who are not “ready?”

I am often asked, “What can we do for high school students who are not “ready?”  I think the question educators are trying to ask is “What can we do when students have unfinished learning?”  This, is a great question because we know this may impact a students’ ability to access the mathematics learning at high levels.  I think the bigger question is, “What can we do when students have unfinished learning so students can have access to mathematics learning at high levels?”

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Remember: The point of the first Shift of Focus is to spend the majority of time on the most important high school content to increase college and career readiness.

We can use the HS Focus document to focus instructional time on the especially and relatively important high school content and widely applicable prerequisite for a range of college majors, postsecondary programs and careers.  The focused instructional time can be used to provide scaffolding to increase access to mathematics learning at high levels.  This does not change the content or duration of a high school course. It redistributes the instructional time to focus on the especially and relatively important high school content.  This shifts the content coverage to an inch-wide and a mile-deep approach.

Below are tips to help implement Focus at the high school level.

Increase these:

  1. Access to high school mathematics standards *
  2. Focusing on the especially and relatively important high school domains, clusters, and standards
  3. Problem solving and communicating reasoning focused on widely applicable prerequisites
  4. Access to the teachers with the most experience or perceived to be most-effective
  5. Scaffolding instruction

Decrease these:

  1. Below grade level mathematics standards *
  2. Covering the standards in a “checklist” approach lacking focus
  3. Problem solving and communicating reasoning applied to complex high school content
  4. Access to the least experience or perceived to be least-effective
  5. Stretching content over two years for the sake of slowing it down

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What about data science, statistics and probability? While I agree, these are highly applicable and relevant content and courses, they are just not the current gatekeeper contents, it’s algebra.  We cannot replace algebra content courses with non-algebra content and hope to increase the college and career readiness for our students.

What about an equivalent course to algebra 2?  Schools are able to place the standards (content) in the high school course as they locally determine. Content is content.  Especially and relatively important high school domains, clusters, and standards emphasis can be differentiated within a course to locally meet the needs of students as well as teaching approach such as a discrete vs integrated approach.  The student learning is the desired outcome.  The only guidance about time we are given in the high school standards is to spend the majority of time on the most important content.

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It is often tempting to lower the expectations for students with unfinished learning because we want to put them on a certain career “pathway.”  I hear it all the time, “but “these” students can’t or they are never going to…”  However, this approach and mind-set does not increase their college and career readiness. We do not know what a students’ future holds or what the world will look like in 10, 20 or 30 years.  Many of our students will have to re-train at some point and we do not mathematics to be the barrier.

I know first-hand what this looks, I was one of “those students.” I began my life in a foster home, was returned to a teenage mom, labeled “at-risk,” had chronic absenteeism (47 days my 7th grade year), put in short-hand and typing classes in hopes I would at least be employable as a secretary. And I was never denied access to mathematics learning at high levels?

While I never used the shorthand, I have found the typing classes to be most helpful in my current role, which no one would have ever predicted for me. But I joined the military for six years, had access to options like education and basic needs, found my inner strength and self-esteem, and now hold a bachelor of science in mathematics.

It was because I had access to “mathematics learning at high levels” in school that mathematics was not a barrier when I returned back to school. I went to school in New York under the Regents program and had access to mathematics learning at high levels”  We should not judge a students’ exit from our schools by their entrance into our schools.

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Schools should refrain from student tracking, teacher tracking, and ensure students have access to mathematics learning at high levels.  We want to equip our students with the high school content they will need to pursue their dreams without their K-12 mathematics learning being a barrier that keeps them from realizing their fullest potential.  Want to make a difference in the life of a student in poverty, give them access to mathematics learning at high levels.  Mathematics learning at high levels allowed me to leave a life of generational poverty. Don’t we want that to be the story for all of our students in Iowa?

In my next blog, I will connect this topic to the 2nd Shift of Coherence and share resources, tools and strategies that can be used.

* the mathematics standards contain additional standards denoted by (+) and are not intended for all students.

 

Do the standards require Algebra 2?

This is likely the question I receive the most.  According to the Iowa Core Mathematics Standards and Standards for Mathematical Practice, there is not a mention of a required Algebra 2 course, or any other high school course for that matter.  Yet, we are talking about this topic more than ever in Iowa and across the country.  I think this is the wrong question. Instead, I am suggesting we reframe the question and ask, “What is required for College and Career Readiness in mathematics.”  In this blog post, I am going to attempt to answer this question.  Disclaimer: Capitalization and other notation may be used grammatically wrong for emphasis.

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The Iowa Core Mathematics Standards and Standards for Mathematical Practice are intended to be ALL standards for ALL students. When we look at the high school standards, some standards have (+)s and these are NOT for all students.  The high school standards are sorted by Domains such as Number and Quantity, Algebra, Functions, Geometry, Statistics and Probability.  Domains are further broken down by Clusters and they may contain one or many standards.  The standards were not intended to create courses or specific approaches such as Algebra 1, Geometry, and Algebra 2 or Integrated. It was the intention to give ACCESS to All students to learn high school mathematics when they are in high school each and every year.

It is up to schools locally to create courses, pathways, etc. This flexibility helps schools promote ACCESS for ALL without lowering expectations and while meeting the needs of students.  This is known as the first Shift for Mathematics, Focus.  Focus means where we are going to spend the majority of our instructional time.  It takes the approach of a mile wide and an inch deep of the past and translates it to the inch wide and mile deep focusing time on the most critical content.

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How much instructional time? Up to 85% on the content highlighted in the Focus documents and 15%  for the rest of the standards.

What domain, cluster and standards? We can use the High School Focus document by Student Achievement Partners, www.achievethecore.org, provides guidance distinguishing between especially important, relatively important and widely applicable. For more on Focus, please see Iowa Math Chats

  • Number and Quantity: N-RN, Real Numbers:
    • Both clusters in this domain contain widely applicable prerequisites.
    • N-Q, Quantities: Every standard in this domain is a widely applicable prerequisite.
    • Note, this domain is especially important in the high school content standards overall as a widely applicable prerequisite.
  • Algebra: Every domain in this category contains widely applicable prerequisites.
    • Note, the A-SSE domain is especially important in the high school content standards overall as a widely applicable prerequisite.
  • Functions: F-IF, Interpreting Functions:
    • Every cluster in this domain contains widely applicable prerequisites.
    • Additionally, standards F-BF.1 and F-LE.1 are relatively important within this category as widely applicable prerequisites.
  • Geometry: 
    • The following standards and clusters are relatively important within this category as widely applicable prerequisites: G-CO.1 G-CO.9 G-CO.10 G-SRT.B G-SRT.C
    • Note, the above standards in turn have learning prerequisites within the Geometry category, including: G-CO.A G-CO.B G-SRT.A
  • Statistics and Probability: 
    • The following standards are relatively important within this category as widely applicable prerequisites: S-ID.2 S-ID.7 S-IC.1
    • Note, the above standards in turn have learning prerequisites within 6-8. SP.
  • Applying Key Takeaways from Grades 6–8**: Solving problems at a level of sophistication appropriate to high school by:
    • Applying ratios and proportional relationships.
    • Applying percentages and unit conversions, e.g., in the context of complicated measurement problems involving quantities with derived or compound units (such as mg/mL, kg/m3 , acre-feet, etc.).
    • Applying basic function concepts, e.g., by interpreting the features of a graph in the context of an applied problem.
    • Applying concepts and skills of geometric measurement e.g., when analyzing a diagram or schematic.
    • Applying concepts and skills of basic statistics and probability (see 6-8.SP). ·
    • Performing rational number arithmetic fluently.

This means there is flexibility so ALL students can have access to the high school mathematics instruction they need. Some students may need more time on especially important, relatively important and widely applicable standards and practices. Some students may need up to 85% of instructional time focused on number and algebra (at the high school level) instead of spending large amounts of times on other standards that are not as important for their college and career readiness.

pump

We want our students to be able to pursue their dreams without mathematics being a barrier.  We know the fewer remedial mathematics courses they take post-secondary, then the more likely it seems they are to persevere with completing programs and degrees. The world we live in becomes more technical each and every day whether in engineering, health care, farming, mechanics, etc., or the military.   Mathematics needs to be the pump into options for our students and not the filter.  We need to remember that it is NOT about courses but about learning.  Learning that will better prepare our students for their future, whatever they may choose.

 

Have the Standards Been Implemented w/ Fidelity?

The main role I have is to help educators in Iowa implement the mathematics standards with fidelity.  It seems like it should be an easy task but it is not. There is so much information out there to sort through, it is hard to know what is the best information to use for where you may be at.   Plus, as educators, we are not all in the same place so what is right for one may not be right for another, whew!

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I have thought a great deal over the last few years and wondered how I could help Iowa educators to have access to the information that they may find useful. And how do I make all of the information that I have access to accessible to Iowa educators.  So, I have come up with all but an original idea to “knowledge transfer” what I have access to to others. Iowa Math Chats – 5 minute video chats where I share everything I know about a topic.  I have wanted to do it for a while and finally I just went for it.

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These Iowa Math Chats are designed for IOWA mathematics educators of any type. I say this because the context is for Iowa and where the work and conversation is. If you are in another state, most of the information is still helpful but know that it was designed for Iowans.

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The first series is a series of what ALL educators need to understand about the 1st Shift of FOCUS. You can read more about all three SHIFTS here. BUT if you don’t have FOCUS  then it is really super difficult to have any  of the other SHIFTS and the Standards of Mathematical Practices. (Capitals are being used intentionally to show emphasis).

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Why these topics on FOCUS? These topics are the most misunderstood when I talk to educators.  Here is why:

1. Many try to implement the standards without paying attention to the Clusters – Clusters – Super Important!

2. If the different types of Clusters are not tended to – then the grade level proficiencies will not happen.

3. If we keep acting like this is new math – the standards are exactly the same math we have always had –  that was the point of the standards – to get rid of all the pneumonics and tricks!! No more “butterfly” math.

4. The Fluencies and the major Clusters make up the Major Work of the Grade – where we should be spending up to 85% of our instructional time on.

5. There are Major Clusters that are a priority and the number of standards vary – prioritizing standards could lead to prioritizing only part of the standards that need to work together in a Cluster and lead to non-proficiency.

Stay tuned for the next series on Coherence! This information is also available on Facebook. Remember to subscribe so you get updates.

What to use for a math intervention?

This has been a really popular question lately as we are well into the school year. What to use for a math intervention? Sometimes educators are looking for a strategy, sometimes a process and sometimes a thing.  I always assure them that if there was a “magic” mathematics anything, I would know about it and be sure to tell them but there isn’t. There are some better rabbit holes for us to go down as we try to find what helps our students learn mathematics and what educators can use to help students “get it,” or get “caught up.” Let us just agree, that those terms in quotes are ambiguous at best.  In  this blog I am going to help you find  a few rabbit holes you may want to explore.

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In previous blogs, I have shared about Number Sense and Learning Trajectories.  I first learned of Learning Trajectories directly from Doug Clements at math SCASS (Math State Collaborative on Assessment and Student Standards), which is the mechanism nationally or how people who have my job get “smart” together about the good stuff to bring back to our individual states. It is put on by CCSSO (Council of Chief State Officers). The same group that brought us the mathematics standards.

Anyways, I didn’t “get it.”  It wasn’t that Doug did a bad job of teaching me, it was  because I had a secondary mathematics background and I didn’t know what I didn’t know.  Which the experience made me realize, I do not know what I need to know about K-5 mathematics. I needed to get “smart” about K-5 mathematics and quick. So I asked some of the AEA consultants, how do I get smart about what I need to know about K-5, and they said take Number Sense from Christina Tondevold.

After taking the Number Sense training, then and only then did I “get it.” Eureka, I understood that I had not had Number Sense myself!  No wonder I didn’t understand the Learning Trajectories I didn’t even understand the 4 early Number Concepts and the 4 Number Relationships (subitizing, verbal counting, object counting, cardinality, spatial relations, 1/2 more/less, benchmarks of 5 & 10, part-part-whole.)  This was the reason that I didn’t understand the Learning Trajectories and how to use them to help students.  But by connecting the  Number Sense learning with the research based Learning Trajectories activities, I realized how powerful they could be to use with students.

This brings us to the topic at hand. Can they be used as a math intervention? An intervention is a combination of program elements or strategies designed to produce behavior changes or improve health status among individuals or an entire population. Educators learning more about Number Sense  and then using Learning Trajectories, to give students experiences to increase their Number Sense  along research based Learning Trajectories could help teachers take students from where they are at to where we want them to be more quickly than perhaps what we are currently doing.

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Example: A student still counting on their fingers may need more subitizing. (I know this because I understand the information in Number Sense .)  I know I need to give the student experiences so I go to the Learning Trajectories and select subitizing and I can get close to where I think the student is at and then work them forward along the subitizing trajectory.  See the screencast here.

A few last tidbits. Number Sense is closing for purchasing individual accounts on October 28, 2019 and will not re-open for a year. Schools purchasing multiple accounts can do so at any time.  The Learning Trajectories are open sourced and you just have to create an account.  I encourage you to watch the video  snippets.  Lastly, for those who are looking for Learning Trajectories more bells and whistle or sophistication in computer program, diagnostics, intervention, be sure to check out Building Blocks or Number Worlds which packages the work of the Learning Trajectories.

I share this information as a potential rabbit hole that you may want to explore. Will we do a better teaching and learning with increase Number Sense ? Yes.  Will we have researched based activities to use with students if we use Learning Trajectories ? Yes. Could this help teachers love to teach math, help students love learning math and help them learn more math? You be the judge. Let me know your thoughts in the comments.