for Mathematicians Andrea Kohlhase Jacobs University, Germany FIZ - - PowerPoint PPT Presentation

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for Mathematicians Andrea Kohlhase Jacobs University, Germany FIZ - - PowerPoint PPT Presentation

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Search Interfaces for Mathematicians Andrea Kohlhase Jacobs University, Germany FIZ Karlsruhe, Germany MathSearch Project FormulaSearch = MathWebSearch How to make best use of it for Mathematicians? Design for Mathematicians? An older

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Search Interfaces for Mathematicians

Andrea Kohlhase

Jacobs University, Germany FIZ Karlsruhe, Germany

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MathSearch Project

FormulaSearch = MathWebSearch How to make best use of it for Mathematicians?

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Design for Mathematicians?

An older version of zbMath ...

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Design for Mathematicians?

vifamath

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Design for Mathematicians?

ResearchGate

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Design for Mathematicians?

mathoverflow

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SLIDE 7

Design for Mathematicians?

MathSciNet

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Design for Mathematicians?

MSC Map

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SLIDE 9

No-Go Questions

  • Which tools are used by

mathematicians for search?

  • What do mathematicians search for?
  • How often do mathematicians search?
  • Which search engines are preferred by

mathematicians?

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The Question at Hand What is „mathematical search“ all about?

(If we understand what mathematical search is all about, then we should know better how to design math search interfaces.)

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Methodology

  • Quantitative Methods? No!
  • Qualitative Methods:

– Questionnaires? – Interviews? – Ethnographic field studies?

  • Semi-Empirical Method:

– Repertory Grid Interviews!

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Repertory Grid Interviews

Exhausting, but unmasking!

adapted

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Repertory Grid Interviews = RGIs

„RGI Elements“

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Repertory Grid Interviews = RGIs

Procedure

  • i. The interviewee randomly chooses three RGI elements.
  • ii. He declares which two of the three elements seem

more similar.

  • iii. He determines the aspect under which these two are

more similar and the aspect under which the third one is different.

  • iv. He evaluates all RGI elements with respect to this

construct.

Similarity Aspect Dissimilarity Aspect

„RGI Construct“

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A Repertory Grid Example

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The RGI Study

Research Mathematicians Info-Services- Mathematicians Non- Mathematicians 11 5 6 Total: 107 Constructs # RGIs: 22 50 Constructs 28 Constructs 29 Constructs Average: 4,54 Average: 5,6 Average: 4,83

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Repertory Grid Interviews = RGIs

Empirical Method = General Procrustes Analysis

1.

Find a consensus grid

(containing “abstract” constructs Con_1 – Con_n):

– comparison of grids wrt the fixed set of RGI elements

2.

Conduct a Principal Components Analysis on the consensus grid

– find the dimensions that differentiate the most between the RGI elements

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Interpretation Tool: Biplot of RGI Elements

Comp 1 Comp 2

zbMath-old arXiv TIB MathSciNet vifamath zbMath-new Catchup Formula- Search Google Scholar Google myOffice myLibrary ResearchGate MSC Map mathoverflow Bibliography myColleagues

1st Principal Component 2nd Principal Component

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Repertory Grid Interviews = RGIs

Empirical Method = General Procrustes Analysis

  • 1. Find consensus grid ...
  • 2. Find Principal Components ...
  • 3. Do a Multiple Groups Components Analysis

– Recompute relative location of real and abstract constructs and visualize them in the biplot

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Interpretation Tool: 3D-Biplot

  • f RGI Elements and -Constructs
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Interpretation Tool: Cluster Analyis in Form of Dendrogram

Con_4_inMATH - ConOpo_4_inMATH Con_4_infoMATH - ConOpo_4_infoMATH Con_6_infoMATH - ConOpo_6_infoMATH Con_2_noMATH - ConOpo_2_noMATH Con_4_noMATH - ConOpo_4_noMATH Con_7_noMATH - ConOpo_7_noMATH Con_2_infoMATH - ConOpo_2_infoMATH Con_3_noMATH - ConOpo_3_noMATH Con_3_inMATH - ConOpo_3_inMATH Con_5_noMATH - ConOpo_5_noMATH Con_5_inMATH - ConOpo_5_inMATH Con_1_infoMATH - ConOpo_1_infoMATH Con_6_inMATH - ConOpo_6_inMATH Con_7_inMATH - ConOpo_7_inMATH Con_8_inMATH - ConOpo_8_inMATH Con_6_noMATH - ConOpo_6_noMATH Con_1_inMATH - ConOpo_1_inMATH Con_5_infoMATH - ConOpo_5_infoMATH Con_2_inMATH - ConOpo_2_inMATH Con_1_noMATH - ConOpo_1_noMATH Con_3_infoMATH - ConOpo_3_infoMATH

1 2 3

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Interpretation Tool: Cluster Analysis in Form of Dendrogram

Con_4_inMATH - ConOpo_4_inMATH Con_4_infoMATH - ConOpo_4_infoMATH Con_6_infoMATH - ConOpo_6_infoMATH Con_2_noMATH - ConOpo_2_noMATH Con_4_noMATH - ConOpo_4_noMATH Con_7_noMATH - ConOpo_7_noMATH Con_2_infoMATH - ConOpo_2_infoMATH Con_3_noMATH - ConOpo_3_noMATH Con_3_inMATH - ConOpo_3_inMATH Con_5_noMATH - ConOpo_5_noMATH Con_5_inMATH - ConOpo_5_inMATH Con_1_infoMATH - ConOpo_1_infoMATH Con_6_inMATH - ConOpo_6_inMATH Con_7_inMATH - ConOpo_7_inMATH Con_8_inMATH - ConOpo_8_inMATH Con_6_noMATH - ConOpo_6_noMATH Con_1_inMATH - ConOpo_1_inMATH Con_5_infoMATH - ConOpo_5_infoMATH Con_2_inMATH - ConOpo_2_inMATH Con_1_noMATH - ConOpo_1_noMATH Con_3_infoMATH - ConOpo_3_infoMATH

1 2 3

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Cluster of what acc. to what?

Con_4_inMATH - ConOpo_4_inMATH Con_4_infoMATH - ConOpo_4_infoMATH Con_6_infoMATH - ConOpo_6_infoMATH Con_2_noMATH - ConOpo_2_noMATH Con_4_noMATH - ConOpo_4_noMATH Con_7_noMATH - ConOpo_7_noMATH Con_2_infoMATH - ConOpo_2_infoMATH Con_3_noMATH - ConOpo_3_noMATH Con_3_inMATH - ConOpo_3_inMATH Con_5_noMATH - ConOpo_5_noMATH Con_5_inMATH - ConOpo_5_inMATH Con_1_infoMATH - ConOpo_1_infoMATH Con_6_inMATH - ConOpo_6_inMATH Con_7_inMATH - ConOpo_7_inMATH Con_8_inMATH - ConOpo_8_inMATH Con_6_noMATH - ConOpo_6_noMATH Con_1_inMATH - ConOpo_1_inMATH Con_5_infoMATH - ConOpo_5_infoMATH Con_2_inMATH - ConOpo_2_inMATH Con_1_noMATH - ConOpo_1_noMATH Con_3_infoMATH - ConOpo_3_infoMATH

Similarity of Constructs

  • acc. to Element Evaluation:

Cluster Analysis of constructs

  • f 3 consensus grids

inMath noMath infoMath

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inMath noMath infoMath

Consensus Grids for 3 Groups

Con_4_inMATH - ConOpo_4_inMATH Con_4_infoMATH - ConOpo_4_infoMATH Con_6_infoMATH - ConOpo_6_infoMATH Con_2_noMATH - ConOpo_2_noMATH Con_4_noMATH - ConOpo_4_noMATH Con_7_noMATH - ConOpo_7_noMATH Con_2_infoMATH - ConOpo_2_infoMATH Con_3_noMATH - ConOpo_3_noMATH Con_3_inMATH - ConOpo_3_inMATH Con_5_noMATH - ConOpo_5_noMATH Con_5_inMATH - ConOpo_5_inMATH Con_1_infoMATH - ConOpo_1_infoMATH Con_6_inMATH - ConOpo_6_inMATH Con_7_inMATH - ConOpo_7_inMATH Con_8_inMATH - ConOpo_8_inMATH Con_6_noMATH - ConOpo_6_noMATH Con_1_inMATH - ConOpo_1_inMATH Con_5_infoMATH - ConOpo_5_infoMATH Con_2_inMATH - ConOpo_2_inMATH Con_1_noMATH - ConOpo_1_noMATH Con_3_infoMATH - ConOpo_3_infoMATH

shared

(2:2:2)

inMATH

(4:1:0)

almost noMATH

(2:3:5)

no noMATH

(1:1:0)

noMATH

(0:1:3)

shared

(1:1:2)

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inMath noMath infoMath

Result 1

Con_4_inMATH - ConOpo_4_inMATH Con_4_infoMATH - ConOpo_4_infoMATH Con_6_infoMATH - ConOpo_6_infoMATH Con_2_noMATH - ConOpo_2_noMATH Con_4_noMATH - ConOpo_4_noMATH Con_7_noMATH - ConOpo_7_noMATH Con_2_infoMATH - ConOpo_2_infoMATH Con_3_noMATH - ConOpo_3_noMATH Con_3_inMATH - ConOpo_3_inMATH Con_5_noMATH - ConOpo_5_noMATH Con_5_inMATH - ConOpo_5_inMATH Con_1_infoMATH - ConOpo_1_infoMATH Con_6_inMATH - ConOpo_6_inMATH Con_7_inMATH - ConOpo_7_inMATH Con_8_inMATH - ConOpo_8_inMATH Con_6_noMATH - ConOpo_6_noMATH Con_1_inMATH - ConOpo_1_inMATH Con_5_infoMATH - ConOpo_5_infoMATH Con_2_inMATH - ConOpo_2_inMATH Con_1_noMATH - ConOpo_1_noMATH Con_3_infoMATH - ConOpo_3_infoMATH

shared

(2:2:2)

inMATH

(4:1:0)

almost noMATH

(2:3:5)

no noMATH

(1:1:0)

noMATH

(0:1:3)

shared

(1:1:2)

„Info-Service-Mathematicians are inbetween“

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inMath noMath infoMath

Result 2

Con_4_inMATH - ConOpo_4_inMATH Con_4_infoMATH - ConOpo_4_infoMATH Con_6_infoMATH - ConOpo_6_infoMATH Con_2_noMATH - ConOpo_2_noMATH Con_4_noMATH - ConOpo_4_noMATH Con_7_noMATH - ConOpo_7_noMATH Con_2_infoMATH - ConOpo_2_infoMATH Con_3_noMATH - ConOpo_3_noMATH Con_3_inMATH - ConOpo_3_inMATH Con_5_noMATH - ConOpo_5_noMATH Con_5_inMATH - ConOpo_5_inMATH Con_1_infoMATH - ConOpo_1_infoMATH Con_6_inMATH - ConOpo_6_inMATH Con_7_inMATH - ConOpo_7_inMATH Con_8_inMATH - ConOpo_8_inMATH Con_6_noMATH - ConOpo_6_noMATH Con_1_inMATH - ConOpo_1_inMATH Con_5_infoMATH - ConOpo_5_infoMATH Con_2_inMATH - ConOpo_2_inMATH Con_1_noMATH - ConOpo_1_noMATH Con_3_infoMATH - ConOpo_3_infoMATH

inMATH

(4:1:0)

no noMATH

(1:1:0)

noMATH

(0:1:3)

Validation of „Mathematicians are special“

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Relevance Ranking

inMath-Specific Constructs

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Relevance Ranking: Interpretation

3D-Biplot

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Relevance Ranking: Interpretation

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Result 3

Meaningful, math-specific evaluation schemes

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More Cluster Analysis ...

Cluster analysis of all elements for

vs.

Which math search interfaces are more similar than others?

inMath noMath

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Mathematicians vs. Non-Mathematicians

Element Clusters

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More Cluster Analysis ...

Cluster analysis of all constructs for

vs.

Which evaluation schemes are more similar than others?

inMath noMath

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inMATH

Construct Clusters

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 Main Result: 10 Patterns

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Pattern (1/10) „Familiarity“:

Mathematicians do not assess math search interfaces based on familiarity.

  • D. Bruff: „Stevenson Center 1210“
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Pattern (2/10) „Community“:

Mathematicians trust human and community resources. More so than other communities and more so the older the mathematician.

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Pattern (3/10) „Finding“:

Finding is the primary mathematical search task. Search Find Browse Surf Solve

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Pattern (4/10)

„Social Interaction Tool“:

Mathematicians appreciate social interaction as a mathematical tool. In particular, it is a mathematical practice to collaborate and exchange feedback.

≠ „Mathematicians are social“!

yes: no,

but maybe:

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Pattern (5/10) „Medium“:

Mathematicians aim at adopting a search tool as a medium. Medium = „Extension of Man“

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Pattern (6/10) „Function“:

Mathematicians appreciate function over form.

koepfedeswandels.wordpress.com

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Pattern (7/10) „Outcome“:

Mathematicians care more for the outcome than the input.

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Pattern (8/10) „Empowerment“:

Mathematicians want to be empowered in the search process.

spiegel.de

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Pattern (9/10) „Transparency“:

Mathematicians base their information search process on transparency of the search result.

themarketingbit.com marlismatthias.blogspot.com

Predicted Precision? Predicted Recall?

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Pattern (10/10) „Expectations“:

Mathematicians expect to find meaningful information in the search result. ≠ meaningful search result!

netztaucher.de

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Summary

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Conclusion

Mathematicians are special, you are probably not any longer a mathematician, make use of the patterns when considering the pros and cons of a design! Old zbMath website and wonderful Google

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Conclusion

New zbMath website: very similar to Google! Mathematicians are special, you are probably not any longer a mathematician, make use of the patterns when considering the pros and cons of a design!

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Conclusion

Very noticeable difference! Mathematicians are special, you are probably not any longer a mathematician, make use of the patterns when considering the pros and cons of a design!

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Conclusion

Mathematicians are special, you are probably not any longer a mathematician, make use of the patterns when considering the pros and cons of a design! No noticeable difference for mathematicians – “not really“!