<PAGE>   1

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                       SECURITIES AND EXCHANGE COMMISSION
                             WASHINGTON, D.C. 20549

                                   FORM 10-Q/A
                                   AMENDMENT 1


(MARK ONE)

 X   QUARTERLY REPORT PURSUANT TO SECTION 13 OR 15(d) OF THE SECURITIES EXCHANGE
---  ACT OF 1934 FOR THE QUARTERLY PERIOD ENDED AUGUST 2, 1997, OR

     TRANSITION REPORT PURSUANT TO SECTION 13 OR 15(d) OF THE SECURITIES
---  EXCHANGE ACT OF 1934 FOR THE TRANSITION PERIOD FROM ________ TO _______.


                         COMMISSION FILE NUMBER 1-12814

                            COLE NATIONAL CORPORATION
             (EXACT NAME OF REGISTRANT AS SPECIFIED IN ITS CHARTER)


          DELAWARE                                     34-1453189
(STATE OR OTHER JURISDICTION OF                    (I.R.S. EMPLOYER
INCORPORATION OR ORGANIZATION)                     DENTIFICATION NO.)


   5915 LANDERBROOK DRIVE
   MAYFIELD HEIGHTS, OHIO                                   44124
(ADDRESS OF PRINCIPAL EXECUTIVE OFFICES)                  (ZIP CODE)

                                  (440)449-4100
              (REGISTRANT'S TELEPHONE NUMBER, INCLUDING AREA CODE)



INDICATE BY CHECK MARK WHETHER THE REGISTRANT (1) HAS FILED ALL REPORTS REQUIRED
TO BE FILED BY SECTION 13 OR 15(D) OF THE SECURITIES EXCHANGE ACT OF 1934 DURING
THE PRECEDING 12 MONTHS (OR FOR SUCH SHORTER PERIOD THAT THE REGISTRANT WAS
REQUIRED TO FILE SUCH REPORTS), AND (2) HAS BEEN SUBJECT TO SUCH FILING
REQUIREMENTS FOR THE PAST 90 DAYS.      X  YES      NO
                                       ---      ---


AS OF AUGUST 29, 1997, 14,724,935 SHARES OF THE REGISTRANT'S CLASS A COMMON
STOCK WERE OUTSTANDING.

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                   COLE NATIONAL CORPORATION AND SUBSIDIARIES
                                   FORM 10-Q/A
                           PERIOD ENDED AUGUST 2, 1997




THIS FORM 10-Q/A AMENDS PART II, ITEM 4 TO REGISTRANT'S FORM 10-Q FOR THE PERIOD
ENDED AUGUST 2, 1997


PART II. OTHER INFORMATION
--------------------------

         ITEM 4. SUBMISSION OF MATTERS TO A VOTE OF SECURITY-HOLDERS

SIGNATURE
---------



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                           PART II - OTHER INFORMATION



ITEM 4. SUBMISSION OF MATTERS TO A VOTE OF SECURITY-HOLDERS

     On June 12, 1997, the Company held its annual meeting of stockholders. At
that meeting, the stockholders elected seven directors to serve until the next
annual meeting of stockholders, approved the Amended and Restated Nonqualified
Stock Option Plan for Non-employee Directors, approved an amendment to the
Certificate of Incorporation to increase the number of authorized shares of
Common Stock, approved an amendment to the Certificate of Incorporation to
increase the number of authorized shares of Preferred Stock, approved the
Non-employee Director Equity and Deferred Compensation Plan, and confirmed the
appointment of Arthur Andersen LLP as independent auditors of the Company for
the fiscal year ending January 31, 1998.

     Of the total eligible votes of 12,051,040, stockholders cast votes of
11,292,562 or 93.7%, of the total eligible votes. The votes cast for the
aforementioned matters were as follows:

     1)   Election of Directors

<TABLE>
<CAPTION>
                                                               Abstentions   
                                                              and/or Broker  
                                        For        Withheld    non-votes     
                                    ----------     --------    ---------     
                                                                             
<S>                                 <C>             <C>            <C>       
          Jeffrey A. Cole           11,157,762      134,800        0         
          Timothy F. Finley         11,157,762      134,800        0         
          Irwin W. Gold             11,156,762      135,800        0         
          Peter V. Handel           11,157,762      134,800        0         
          Charles A. Ratner         11,157,762      134,800        0         
          Walter J. Salmon          11,157,762      134,800        0         
          Brian B. Smith            11,156,362      136,200        0         
</TABLE>  

     2)   Amended and Restated Nonqualified Stock Option Plan for Non-employee
          Directors

<TABLE>
<CAPTION>
                                                            Abstentions
                                                           and/or Broker
                                      For        Withheld    non-votes
                                   ----------     --------    ---------     
<S>                                <C>            <C>          <C>   
          Approval of Plan         11,168,597     101,027      22,938
</TABLE>

     3)   Amendment to Certificate of Incorporation to increase the number of
          authorized shares of Common Stock

<TABLE>
<CAPTION>
                                                            Abstentions
                                                           and/or Broker
                                      For        Withheld    non-votes
                                   ----------     --------    ---------     
<S>                                <C>            <C>          <C>   
          Approval of Amendment    10,909,713     362,452      20,397
</TABLE>

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<PAGE>   4

     4)   Amendment to Certificate of Incorporation to increase the number of
          authorized shares of Preferred Stock

<TABLE>
<CAPTION>
                                                            Abstentions
                                                           and/or Broker
                                      For        Withheld    non-votes
                                   ----------    --------    ---------     
<S>                                <C>            <C>          <C>   
          Approval of Amendment    7,277,436      2,236,604    445,547
</TABLE>


     5)   Non-employee Director Equity and Deferred Compensation Plan

<TABLE>
<CAPTION>
                                                            Abstentions
                                                           and/or Broker
                                      For        Withheld    non-votes
                                   ----------     --------    ---------     
<S>                               <C>             <C>         <C>   
          Approval of Plan        11,162,813      90,860      25,106
</TABLE>

     6)   Confirmation of Independent Auditors

<TABLE>
<CAPTION>
                                                           Abstentions
                                                          and/or Broker
                                     For        Withheld    non-votes
                                  ----------     --------    ---------     
<S>                               <C>             <C>         <C>   
          Arthur Andersen LLP     11,270,490       2,304      19,768
</TABLE>



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                                    SIGNATURE
                                    ---------

     Pursuant to the requirements of the Securities Exchange Act of 1934, the
registrant has duly caused this report to be signed on its behalf by the
undersigned, thereunto duly authorized.


                               COLE NATIONAL CORPORATION



                               By:      /s/ Wayne L. Mosley
                                   ----------------------------------------
                                   Wayne L. Mosley
                                   Vice President and Controller
                                   (Duly Authorized Officer and Principal
                                   Accounting Officer)

                             Date: October 30, 1997



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